Signal transmission method and apparatus using codebook in wireless communication system supporting multiple antennas

ABSTRACT

The present invention relates to a method for transmitting, by a base station, a downlink signal using a plurality of transmission antennas comprises the steps of: applying a precoding matrix indicated by the PMI, received from a terminal, in a codebook to a plurality of layers, and transmitting the precoded signal to the terminal through a plurality of transmission antennas. Among precoding matrices included in the codebook, a precoding matrix for even number transmission layers can be a 2×2 matrix containing four matrices (W1s), the matrix (W1) having rows of a number of transmission antennas and columns of half the number of transmission layers, the first and second columns of the first row in the 2×2 matrix being multiplied by 1, the first column of the second row being multiplied by coefficient “a” of a phase, and the first column of the second row being multiplied by “−a”.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/133,506, filed on Apr. 20, 2016, now U.S. Pat. No. 9,806,779, whichis a continuation of U.S. application Ser. No. 14/310,174, filed on Jun.20, 2014, now U.S. Pat. No. 9,363,000, which is a continuation of U.S.application Ser. No. 13/639,991, filed on Dec. 10, 2012, now U.S. Pat.No. 8,792,586, which is the National Stage filing under 35 U.S.C. 371 ofInternational Application No. PCT/KR2011/002488, filed on Apr. 8, 2011,which claims the benefit of U.S. Provisional Application No. 61/321,887,filed on Apr. 8, 2010, and 61/324,295, filed on Apr. 14, 2010, thecontents of which are all hereby incorporated by reference herein intheir entirety.

TECHNICAL FIELD

The present invention relates to a wireless communication system, andmore particularly to a method and apparatus for transmitting signalsusing a codebook in a wireless communication system supporting multipleantennas.

BACKGROUND ART

Generally, Multiple-Input Multiple-Output (MIMO) technology willhereinafter be described in detail. In brief, MIMO is an abbreviationfor Multiple Input Multiple Output. MIMO technology uses multipletransmit (Tx) antennas and multiple receive (Rx) antennas to improve theefficiency of transmit/receive (Tx/Rx) of data, whereas the conventionalart generally uses a single transmit (Tx) antenna and a single receive(Rx) antenna. In other words, MIMO technology allows a transmitting endand a receiving end to use multiple antennas so as to increase capacityor improve performance. If necessary, the MIMO technology may also becalled multi-antenna technology.

In order to support MIMO transmission, a precoding matrix that properlydistributes transmission information according to a channel conditionand the like can be used. The conventional 3GPP system supports amaximum of 4Tx antennas for downlink transmission, and defines aprecoding codebook for a maximum of 4Tx antennas.

DISCLOSURE Technical Problem

Accordingly, the present invention is directed to a method and apparatusfor transmitting signals using a codebook in a wireless communicationsystem supporting multiple antennas that substantially obviate one ormore problems due to limitations and disadvantages of the related art.

In a legacy 3GPP LTE system (for example, a system of 3GPP LTE Release 8or 9), a codebook for supporting a maximum of 4 transmit (Tx) antennason downlink has been designed. The 3GPP LTE-A system evolved from thelegacy 3GPP LTE is configured to use the extended antenna structure forimproved performance (for example, improved spectral efficiency), andcan support a maximum of 8Tx antennas on downlink. In order to providehigher throughput, a closed loop MIMO scheme for 8Tx-antennas downlinktransmission can be used. In addition, in order to reduce the amount ofchannel information feedback overhead, a closed-loop MIMO scheme basedon a predefined codebook may be used. Therefore, there is a need todesign a precoding codebook capable of providing superior performance todownlink transmission based on a maximum of 8 transmit (Tx) antennas.

An object of the present invention is to provide a method and apparatusfor transmitting signals using a codebook capable of efficientlysupporting MIMO transmission supporting an extended antennaconfiguration. Another object of the present invention is to provide amethod and apparatus for transmitting signals using a codebook thatreduces feedback overhead and at the same time maintains systemperformance for MIMO transmission based on a plurality of Tx antennas.

It will be appreciated by persons skilled in the art that the objectsthat can be achieved through the present invention are not limited towhat has been particularly described hereinabove and the above and otherobjects that the present invention can achieve will be more clearlyunderstood from the following detailed description taken in conjunctionwith the accompanying drawings.

Technical Solution

The object of the present invention can be achieved by providing amethod for transmitting a downlink signal using 2·N (N is a naturalnumber) transmit (Tx) antennas by a base station (BS) including:receiving a first precoding matrix index (PMI) and a second precodingmatrix index (PMI) from a user equipment (UE); determining a precodingmatrix indicated by a combination of the first PMI and the second PMI onthe basis of a prestored codebook; performing precoding by applying thedetermined precoding matrix to the downlink signal mapped to R layers(where 1≤R≤8); and transmitting the precoded signal to the userequipment (UE) through 2·N Tx antennas, wherein the prestored codebookincludes precoding matrices configured in the form of

$\begin{bmatrix}W_{1} & W_{1} \\{aW}_{1} & {- {aW}_{1}}\end{bmatrix}\quad$when R is an even number, where W₁ is an N×(R/2) matrix and a is acoefficient of a phase.

In another aspect of the present invention, a method for processing adownlink signal using 2·N (N is a natural number) transmit (Tx) antennasby a user equipment (UE) includes transmitting a first precoding matrixindex (PMI) and a second precoding matrix index (PMI) indicating aprecoding matrix selected from a prestored codebook to a base station(BS); receiving the downlink signal, that is mapped to R layers (where1≤R≤8), is precoded by a precoding matrix indicated by a combination ofthe first and second PMIs, and is then transmitted through the 2·N Txantennas, from the base station (BS); and processing the downlink signalusing the precoding matrix, wherein the prestored codebook includesprecoding matrices configured in the form of

$\begin{bmatrix}W_{1} & W_{1} \\{aW}_{1} & {- {aW}_{1}}\end{bmatrix}\quad$when R is an even number, where W₁ is an N×(R/2) matrix and a is acoefficient of a phase.

In another aspect of the present invention, a base station (BS) fortransmitting a downlink signal includes: 2·N (N is a natural number)transmit (Tx) antennas; a transmission (Tx) module for transmitting thedownlink signal to a user equipment (UE) through the 2·N Tx antennas; areception (Rx) module for receiving an uplink signal from the userequipment (UE); a memory for storing a codebook including a precodingmatrix; and a processor for controlling the base station (BS), whereinthe processor enables the reception (x) module to receive a firstprecoding matrix index (PMI) and a second precoding matrix index (PMI)from a user equipment (UE), determines a precoding matrix indicated by acombination of the first PMI and the second PMI on the basis of thecodebook stored in the memory, maps the downlink signal to R layers(where 1≤R≤8), performs precoding by applying the determined precodingmatrix to the downlink signal mapped to the R layers, and allows thetransmission (Tx) module to transmit the precoded signal to the userequipment (UE) through 2·N Tx antennas, and wherein the prestoredcodebook includes precoding matrices configured in the form of

$\quad\begin{bmatrix}W_{1} & W_{1} \\{aW}_{1} & {- {aW}_{1}}\end{bmatrix}$when R is an even number, where W₁ is an N×(R/2) matrix and a is acoefficient of a phase.

In another aspect of the present invention, a user equipment (UE) forprocessing a downlink signal received from a base station (BS) including2·N (N is a natural number) transmit (Tx) antennas includes: a reception(Rx) module for receiving the downlink signal from the base station(BS); a transmission (Tx) module for transmitting an uplink signal tothe base station (BS); a memory for storing a codebook including aprecoding matrix; and a processor for controlling the user equipment(UE), wherein the processor enables the transmission (Tx) module totransmit a first precoding matrix index (PMI) and a second precodingmatrix index (PMI) indicating a precoding matrix selected from acodebook prestored in the memory to a base station (BS); enables thereception (Rx) module to receive the downlink signal, that is mapped toR layers (where 1≤R≤8), is precoded by a precoding matrix indicated by acombination of the first and second PMIs, and is then transmittedthrough the 2·N Tx antennas, from the base station (BS); and processesthe downlink signal using the precoding matrix, and wherein theprestored codebook includes precoding matrices configured in the form of

$\quad\begin{bmatrix}W_{1} & W_{1} \\{aW}_{1} & {- {aW}_{1}}\end{bmatrix}$when R is an even number, where W₁ is an N×(R/2) matrix and a is acoefficient of a phase.

W₁ may be a Discrete Fourier Transform (DFT) matrix.

If R is an even number, W₁ may be configured as a matrix of [v1 . . .v(R/2)], and each of v1 . . . v(R/2) may be an N×1 matrix.

Each of v1 . . . v(R/2) may be configured as a DFT matrix.

If R is equal to 4 (R=4), W₁ may be configured in the form of

$\quad\begin{bmatrix}{v\; 1} & {v\; 2} & {\;{v\; 1}} & {v\; 2} \\{{a \cdot v}\; 1} & {{a \cdot v}\; 2} & {{{- a} \cdot v}\; 1} & {{{- a} \cdot v}\; 2}\end{bmatrix}$

If R is denoted by 3≤R≤7, the precoding matrix of the R layers may becomprised of a column subset of precoding matrices of (R+1) layers.

N may be set to 4 (N=4).

It is to be understood that both the foregoing general description andthe following detailed description of the present invention areexemplary and explanatory and are intended to provide furtherexplanation of the invention as claimed.

Advantageous Effects

Exemplary embodiments of the present invention have the followingeffects. The embodiments of the present invention can provide a methodand apparatus for transmitting signals using a codebook capable ofefficiently supporting MIMO transmission supporting an extended antennaconfiguration. The embodiments of the present invention can also providea method and apparatus for transmitting signals using a codebook thatreduces feedback overhead and at the same time maintains systemperformance for MIMO transmission based on a plurality of Tx antennas.

It will be appreciated by persons skilled in the art that the effectsthat can be achieved through the present invention are not limited towhat has been particularly described hereinabove and other advantages ofthe present invention will be more clearly understood from the followingdetailed description taken in conjunction with the accompanyingdrawings.

DESCRIPTION OF DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention, illustrate embodiments of the inventionand together with the description serve to explain the principle of theinvention.

FIG. 1 is a conceptual diagram illustrating a downlink radio framestructure.

FIG. 2 exemplarily shows a resource grid of a downlink (DL) slot.

FIG. 3 exemplarily shows a downlink (DL) frame structure.

FIG. 4 exemplarily shows an uplink (UL) subframe structure for use in asystem.

FIG. 5 exemplarily shows a common reference signal (CRS) pattern.

FIG. 6 exemplarily shows a reference signal pattern shift.

FIGS. 7 and 8 exemplarily show a resource element group (REG) serving asan allocation unit of a downlink control channel.

FIG. 9 is a conceptual diagram illustrating a Physical Control FormatIndicator Channel (PCFICH) transmission scheme.

FIG. 10 shows the positions of a PCFICH and a Physical hybrid ARQindicator Channel (PHICH).

FIG. 11 shows a downlink resource element position mapped to a PHICHgroup.

FIG. 12 is a block diagram illustrating a transmitter for use in aSingle Carrier Frequency-Division Multiple Access (SC-FDMA) system.

FIG. 13 shows a signal mapping scheme in which a DFT processed signal ismapped to a frequency domain.

FIG. 14 is a conceptual diagram illustrating a method for transmitting areference signal.

FIG. 15 shows the position of a symbol mapped to a reference signal.

FIGS. 16 to 19 are conceptual views illustrating the clusteredDFT-s-OFDMA scheme.

FIG. 20 is a block diagram illustrating a MIMO system.

FIG. 21 is a functional block diagram illustrating a MIMO system.

FIG. 22 is a conceptual diagram illustrating codebook based precoding.

FIG. 23 exemplarily shows 8 transmit (Tx) antennas.

FIGS. 24 to 43 show antenna responses according to examples of thepresent invention.

FIG. 44 is a flowchart illustrating a MIMO transmission and receptionmethod according to embodiments of the present invention.

FIG. 45 is a block diagram illustrating a base station (BS) and a userequipment (UE) applicable to embodiments of the present invention.

BEST MODE

The following embodiments are proposed by combining constituentcomponents and characteristics of the present invention according to apredetermined format. The individual constituent components orcharacteristics should be considered optional on the condition thatthere is no additional remark. If required, the individual constituentcomponents or characteristics may not be combined with other componentsor characteristics. Also, some constituent components and/orcharacteristics may be combined to implement the embodiments of thepresent invention. The order of operations to be disclosed in theembodiments of the present invention may be changed. Some components orcharacteristics of any one embodiment may also be included in otherembodiments, or may be replaced with those of the other embodiments asnecessary.

The embodiments of the present invention are disclosed on the basis of adata communication relationship between a base station and a terminal.In this case, the base station is a terminal node of a network via whichthe base station can directly communicate with the terminal. Specificoperations to be conducted by the base station in the present inventionmay also be conducted by an upper node of the base station as necessary.

In other words, it will be obvious to those skilled in the art thatvarious operations for enabling the base station to communicate with theterminal in a network composed of several network nodes including thebase station will be conducted by the base station or other networknodes other than the base station. The term “Base Station (BS)” may bereplaced with the terms fixed station, Node-B, eNode-B (eNB), or accesspoint as necessary. In addition, the term “Base Station (BS)” mayinclude the concept of a cell or sector. The term “relay” may bereplaced with the terms a Relay Node (RN) or Relay Station (RS). Theterm “terminal” may also be replaced with the terms User Equipment (UE),Mobile Station (MS), Mobile Subscriber Station (MSS) or SubscriberStation (SS) as necessary. While the following description exemplarilyuses a UE or a relay node (RN) as an uplink transmission entity andexemplarily uses a BS (eNB) or RN as an uplink reception entity, thescope or spirit of the present invention is not limited thereto.Similarly, the downlink transmission entity may be a BS or RN and thedownlink reception entity may be a UE or RN. In other words, uplinktransmission may indicate transmission from the UE to the BS,transmission from the UE to the RN, or transmission from the RN to theBS. Similarly, downlink transmission may indicate transmission from theBS to the UE, transmission from the BS to the RN, or transmission fromthe RN to the UE.

It should be noted that specific terms disclosed in the presentinvention are proposed for convenience of description and betterunderstanding of the present invention, and the use of these specificterms may be changed to another format within the technical scope orspirit of the present invention.

In some instances, well-known structures and devices are omitted inorder to avoid obscuring the concepts of the present invention andimportant functions of the structures and devices are shown in blockdiagram form. The same reference numbers will be used throughout thedrawings to refer to the same or like parts.

Exemplary embodiments of the present invention are supported by standarddocuments disclosed for at least one of wireless access systemsincluding an Institute of Electrical and Electronics Engineers (IEEE)802 system, a 3^(rd) Generation Project Partnership (3GPP) system, a3GPP Long Term Evolution (LTE) system, an LTE-Advanced (LTE-A) system,and a 3GPP2 system. In particular, the steps or parts, which are notdescribed to clearly reveal the technical idea of the present invention,in the embodiments of the present invention may be supported by theabove documents. All terminology used herein may be supported by atleast one of the above-mentioned documents.

The following embodiments of the present invention can be applied to avariety of wireless access technologies, for example, CDMA (CodeDivision Multiple Access), FDMA (Frequency Division Multiple Access),TDMA (Time Division Multiple Access), OFDMA (Orthogonal FrequencyDivision Multiple Access), SC-FDMA (Single Carrier Frequency DivisionMultiple Access), and the like. CDMA may be embodied with wireless (orradio) technology such as UTRA (Universal Terrestrial Radio Access) orCDMA2000. TDMA may be embodied with wireless (or radio) technology suchas GSM (Global System for Mobile communications)/GPRS (General PacketRadio Service)/EDGE (Enhanced Data Rates for GSM Evolution). OFDMA maybe embodied with wireless (or radio) technology such as Institute ofElectrical and Electronics Engineers (IEEE) 802.11 (Wi-Fi), IEEE 802.16(WiMAX), IEEE 802-20, and E-UTRA (Evolved UTRA). UTRA is a part of UMTS(Universal Mobile Telecommunications System). 3GPP (3rd GenerationPartnership Project) LTE (long term evolution) is a part of E-UMTS(Evolved UMTS), which uses E-UTRA. 3GPP LTE employs OFDMA in downlinkand employs SC-FDMA in uplink. LTE-Advanced (LTE-A) is an evolvedversion of 3GPP LTE. WiMAX can be explained by IEEE 802.16e(WirelessMAN-OFDMA Reference System) and advanced IEEE 802.16m(WirelessMAN-OFDMA Advanced System). For clarity, the followingdescription focuses on 3GPP LTE and 3GPP LTE-A. However, technicalfeatures of the present invention are not limited thereto.

FIG. 1 exemplarily shows a radio frame structure for use in a 3rdGeneration Partnership Project Long Term Evolution (3GPP LTE) system. Adownlink (DL) radio frame structure will hereinafter be described withreference to FIG. 1.

In a cellular Orthogonal Frequency Division Multiplexing (OFDM) radiopacket communication system, uplink/downlink data packet transmission isperformed in subframe units. One subframe is defined as a predeterminedtime interval including a plurality of OFDM symbols. 3GPP LTE supports atype 1 radio frame structure applicable to Frequency Division Duplexing(FDD) and a type 2 radio frame structure applicable to Time DivisionDuplexing (TDD).

FIG. 1(a) is a diagram showing the structure of the type 1 radio frame.A downlink radio frame includes 10 subframes, and one subframe includestwo slots in a time domain. A time required for transmission of onesubframe is defined in a Transmission Time Interval (TTI). For example,one subframe may have a length of 1 ms and one slot may have a length of0.5 ms. One slot may include a plurality of OFDM symbols in a timedomain and include a plurality of Resource Blocks (RBs) in a frequencydomain. Since 3GPP LTE uses OFDMA in downlink, the OFDM symbol indicatesone symbol duration. The OFDM symbol may be called an SC-FDMA symbol ora symbol duration. RB is a resource allocation unit and includes aplurality of contiguous carriers in one slot.

The number of OFDM symbols included in one slot may be changed accordingto the configuration of a Cyclic Prefix (CP). The CP includes anextended CP and a normal CP. For example, if the OFDM symbols areconfigured by the normal CP, the number of OFDM symbols included in oneslot may be seven. If the OFDM symbols are configured by the extendedCP, the length of one OFDM symbol is increased, the number of OFDMsymbols included in one slot is less than that of the case of the normalCP. In case of the extended CP, for example, the number of OFDM symbolsincluded in one slot may be six. If the channel state is unstable, forexample, if a User Equipment (UE) moves at a high speed, the extended CPmay be used in order to further reduce inter-symbol interference.

In case of using the normal CP, since one slot includes seven OFDMsymbols, one subframe includes 14 OFDM symbols. At this time, the firsttwo or three OFDM symbols of each subframe may be allocated to aPhysical Downlink Control Channel (PDCCH) and the remaining OFDM symbolsmay be allocated to a Physical Downlink Shared Channel (PDSCH).

The structure of a type 2 radio frame is shown in FIG. 1(b). The type 2radio frame includes two half-frames, each of which is made up of fivesubframes, a downlink pilot time slot (DwPTS), a guard period (GP), andan uplink pilot time slot (UpPTS), in which one subframe consists of twoslots. That is, one subframe is composed of two slots irrespective ofthe radio frame type. DwPTS is used to perform initial cell search,synchronization, or channel estimation. UpPTS is used to perform channelestimation of a base station and uplink transmission synchronization ofa user equipment (UE). The guard interval (GP) is located between anuplink and a downlink so as to remove interference generated in uplinkdue to multi-path delay of a downlink signal. That is, one subframe iscomposed of two slots irrespective of the radio frame type.

The structure of the radio frame is only exemplary. Accordingly, thenumber of subframes included in the radio frame, the number of slotsincluded in the subframe or the number of symbols included in the slotmay be changed in various manners.

FIG. 2 is a diagram showing an example of a resource grid in onedownlink slot. OFDM symbols are configured by the normal CP. Referringto FIG. 2, the downlink slot includes a plurality of OFDM symbols in atime domain and includes a plurality of RBs in a frequency domain.Although one downlink slot includes seven OFDM symbols and one RBincludes 12 subcarriers, the present invention is not limited thereto.Each element of the resource grid is referred to as a Resource Element(RE). For example, an RE a(k,l) is located at a k-th subcarrier and anl-th OFDM symbol. In case of the normal CP, one RB includes 12×7 REs (incase of the extended CP, one RB includes 12×6 REs). Since a distancebetween subcarriers is 15 kHz, one RB includes about 180 kHz in thefrequency region. N^(DL) denotes the number of RBs included in thedownlink slot. The N^(DL) is determined based on downlink transmissionbandwidth set by scheduling of a base station (BS).

FIG. 3 is a diagram showing the structure of a downlink subframe. Amaximum of three OFDM symbols of a front portion of a first slot withinone subframe corresponds to a control region to which a control channelis allocated. The remaining OFDM symbols correspond to a data region towhich a Physical Downlink Shared Channel (PDSCH) is allocated. The basicunit of transmission becomes one subframe. That is, a PDCCH and a PDSCHare allocated to two slots. Examples of the downlink control channelsused in the 3GPP LTE system include, for example, a Physical ControlFormat Indicator Channel (PCFICH), a Physical Downlink Control Channel(PDCCH), a Physical Hybrid automatic repeat request Indicator Channel(PHICH), etc. The PCFICH is transmitted at a first OFDM symbol of asubframe, and includes information about the number of OFDM symbols usedto transmit the control channel in the subframe. The PHICH includes aHARQ ACK/NACK signal as a response to uplink transmission. The controlinformation transmitted through the PDCCH is referred to as DownlinkControl Information (DCI). The DCI includes uplink or downlinkscheduling information or an uplink transmit power control command for acertain UE group. The PDCCH may include resource allocation andtransmission format of a Downlink Shared Channel (DL-SCH), resourceallocation information of an Uplink Shared Channel (UL-SCH), paginginformation of a Paging Channel (PCH), system information on the DL-SCH,resource allocation of a higher layer control message such as a RandomAccess Response (RAR) transmitted on the PDSCH, a set of transmit powercontrol commands for individual UEs in a certain UE group, transmitpower control information, activation of Voice over IP (VoIP), etc. Aplurality of PDCCHs may be transmitted within the control region. The UEmay monitor the plurality of PDCCHs. The PDCCHs are transmitted on anaggregation of one or several contiguous control channel elements(CCEs). The CCE is a logical allocation unit used to provide the PDCCHsat a coding rate based on the state of a radio channel. The CCEcorresponds to a plurality of resource element groups. The format of thePDCCH and the number of available bits are determined based on acorrelation between the number of CCEs and the coding rate provided bythe CCEs. The base station determines a PDCCH format according to a DCIto be transmitted to the UE, and attaches a Cyclic Redundancy Check(CRC) to control information. The CRC is masked with a Radio NetworkTemporary Identifier (RNTI) according to an owner or usage of the PDCCH.If the PDCCH is for a specific UE, a cell-RNTI (C-RNTI) of the UE may bemasked to the CRC. Alternatively, if the PDCCH is for a paging message,a paging indicator identifier P-RNTI) may be masked to the CRC. If thePDCCH is for system information (more specifically, a system informationblock (SIB)), a system information identifier and a system informationRNTI (SI-RNTI) may be masked to the CRC. To indicate a random accessresponse that is a response for transmission of a random access preambleof the UE, a random access-RNTI (RA-RNTI) may be masked to the CRC.

FIG. 4 is a diagram showing the structure of an uplink frame. The uplinksubframe may be divided into a control region and a data region in afrequency domain. A Physical Uplink Control Channel (PUCCH) includinguplink control information is allocated to the control region. APhysical uplink Shared Channel (PUSCH) including user data is allocatedto the data region. In order to maintain single carrier characteristics,one UE does not simultaneously transmit the PUCCH and the PUSCH. ThePUCCH for one UE is allocated to an RB pair in a subframe. RBs belongingto the RB pair occupy different subcarriers with respect to two slots.Thus, the RB pair allocated to the PUCCH is “frequency-hopped” at a slotedge.

Reference Signal

In a MIMO system, each transmission antenna has an independent datachannel. A receiver estimates a channel with respect to eachtransmission antenna and receives data transmitted from eachtransmission antenna. Channel estimation refers to a process ofcompensating for signal distortion due to fading so as to restore thereceived signal. Fading refers to a phenomenon in which the intensity ofa signal is rapidly changed due to multi-path delay and time delay in awireless communication system environment. For channel estimation, areference signal known to both a transmitter and a receiver isnecessary. The reference signal may be abbreviated to RS or referred toas a pilot signal according to the standard used.

The legacy 3GPP LTE Release-8 or Release-9 has defined a downlinkreference signal transmitted from the base station (BS). A downlinkreference signal is a pilot signal for coherent demodulation, such as aPhysical Downlink Shared Channel (PDSCH), a Physical Control FormatIndicator Channel (PCFICH), a Physical Hybrid Indicator Channel (PHICH),and a Physical Downlink Control Channel (PDCCH). The downlink referencesignal includes a Common Reference Signal (CRS) shared among all UEs ina cell and a Dedicated Reference Signal (DRS) for a specific UE. The CRSmay be referred to as a cell-specific reference signal. The DRS may bereferred to as a UE-specific reference signal or a DemodulationReference Signal (DMRS).

A downlink reference signal (DRS) allocation scheme for use in a legacy3GPP LTE system will hereinafter be described in detail. The resourceelement position (i.e., a reference signal pattern) to which a referencesignal is transmitted will hereinafter be described on the basis of asingle resource block (i.e., the length of one subframe in a time domainx the length of 12 subcarriers in a frequency domain). One subframe iscomposed of 14 OFDM symbols (in case of a normal CP), or is composed of12 OFDM symbols (in case of an extended CP). The number of subcarriersin one OFDM symbol is set to one of 128, 256, 512, 1024, 1536, or 2048.

FIG. 5 shows a common reference signal (CRS) pattern when one TTI (i.e.,one subframe) includes 14 OFDM symbols. FIG. 5(a) shows a CRS patternfor use in a system having one Tx (1Tx) transmit antenna, FIG. 5(b)shows a CRS pattern for use in a system having 2 Tx antennas, and FIG.5(c) shows a CRS pattern for use in a system having 4 Tx antennas.

In FIG. 5, R0 is a reference signal for an antenna port index #0. InFIG. 5, R1 is a reference signal of an antenna port index #1, R2 is areference signal of an antenna port index #2, and R3 is a referencesignal of an antenna port index #3. No signal is transmitted to theposition of an RE to which a reference signal for each antenna port istransmitted, such that interference is prevented from occurring in theremaining antenna ports other than a specific antenna port where areference signal is transmitted.

FIG. 6 shows that a reference signal pattern is shifted per cell so asto prevent reference signals of a plurality of cells from colliding.Assuming that a reference signal pattern of a single antenna port isused at Cell #1 of FIG. 6, a reference signal pattern is shifted inunits of a subcarrier or OFDM symbol so as to prevent reference signalsof Cell #2 and Cell #3 contiguous to Cell #1 from colliding with eachother, such that it can protect the reference signal. For example, incase of 1Tx antenna transmission, a reference signal is located on asingle OFDM symbol at intervals of 6 subcarriers, such that at least 5contiguous cells may locate their reference signals at differentresource elements under the condition that shifting is applied to eachcell on the basis of a frequency-domain subcarrier. For example,frequency shift of a reference signal can be represented by Cells #2˜#6of FIG. 6.

In addition, a Pseudo-Random (PN) sequence is multiplied by a downlinkreference signal per cell, and is then transmitted, so that the receivercan reduce interference caused by a reference signal received from acontiguous cell, resulting in an increase in channel estimationperformance. The PN sequence can be applied in units of an OFDM symbolof a single subframe. In addition, different PN sequences can be appliedto a cell ID, a subframe number, and OFDM symbol positions.

In case of the improved system (for example, a wireless communicationsystem (e.g., 3GPP LTE Release-10 or subsequent release) supporting 8 Txantennas) having an extended antenna structure as compared to the legacycommunication system (for example, a 3GPP LTE Release 8 or 9 system)supporting 4 Tx antennas, DMRS-based data demodulation has beenconsidered to support not only efficient reference signal management butalso the developed transmission scheme. That is, DMRS for at least twolayers can be defined to support data transmission through an extendedantenna. Since DMRS is precoded by the same precoder as that of data,the receiver can easily estimate channel information for datademodulation without using separate precoding information. In themeantime, whereas a downlink receiver can obtain precoded channelinformation for the extended antenna structure through a DMRS, aseparate reference signal other than the DMRS is needed to obtainnon-precoded channel information. Therefore, LTE-A can define areference signal (i.e., CSI-RS) for obtaining channel state information(CSI) from a receiver. CSI-RS can be transmitted through 8 antennaports. In order to discriminate between an antenna port to which CSI-RSis transmitted and an antenna port of the legacy 3GPP LTE Release 8/9,antenna port indices #15˜#22 can be used.

Downlink Control Channel Structure

The first three OFDM symbols for each subframe can be basically used asa transmission region of a downlink control channel, and the first tothird OFDM symbols may be used according to overhead of a downlinkcontrol channel. PCFICH may be used to adjust the number of OFDM symbolsfor a downlink control channel per subframe. In order to provideacknowledgement/negative acknowledgment (ACK/NACK) information foruplink transmission on downlink, a Physical Hybrid-automatic repeatrequest (ARQ) Indicator Channel (PHICH) may be used. In addition, aPDCCH may be used to transmit either control information for downlinkdata transmission or control information for uplink data transmission.

FIGS. 7 and 8 exemplarily show that the above-mentioned downlink controlchannels are allocated in units of a resource element group (REG) in acontrol region for each subframe. In more detail, FIG. 7 shows a systemhaving 1Tx antenna or 2Tx antennas, and FIG. 8 shows a system having 4Txantennas. As can be seen from FIGS. 7 and 8, an REG serving as a basicresource unit to which a control channel is allocated is composed of 4concatenated resource elements (REs) in a frequency domain other thansome REs to which reference signals are allocated. A predeterminednumber of REGs may be used to transmit a downlink control channelaccording to downlink control channel (DCH) overhead.

PCFICH (Physical Control Format Indicator Channel)

In order to provide resource allocation information or the like of thecorresponding subframe to each subframe, a PDCCH may be transmittedamong OFDM symbol indices #0 to #2. In accordance with overhead of acontrol channel, an OFDM symbol index #0 may be used, OFDM symbolindices #0 and #1 may be used, or OFDM symbol indices #0 to #2 may beused. The number of OFDM symbols used by a control channel may bechanged per subframe, and information regarding the number of OFDMsymbols may be provided over a PCFICH. Therefore, PCFICH must betransmitted per subframe.

Three kinds of information can be provided through a PCFICH. Thefollowing Table 1 shows a Control Format Indicator of a PCFICH. CFI=1denotes that a PDCCH is transmitted at OFDM symbol index #0, CFI=2denotes that a PDCCH is transmitted at OFDM symbol indices #0 and #1,and CFI=3 denotes that a PDCCH is transmitted at OFDM symbol indices #0to #2.

TABLE 1 CFI codeword CFI <b₀, b₁, . . . , b₃₁> 1 <0, 1, 1, 0, 1, 1, 0,1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,1> 2 <1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1,0, 1, 1, 0, 1, 1, 0, 1, 1, 0> 3 <1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1,1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1> 4 <0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0> (Reserved)

Information transmitted over a PCFICH may be differently definedaccording to system bandwidth. For example, if a system bandwidth isless than a specific threshold value, CFI=1, CFI=2, and CFI=3 mayindicate that two OFDM symbols, three OFDM symbols, and four OFDMsymbols are used for a PDCCH, respectively.

FIG. 9 is a conceptual diagram illustrating a PCFICH transmissionscheme. An REG shown in FIG. 9 may be composed of 4 subcarriers, and maybe composed only of data subcarriers other than a reference signal (RS).Generally, a transmit diversity scheme may be applied to the REG Toprevent inter-cell interference of the PCFICH, the REGs to which thePCFICH is mapped may be shifted per cell in the frequency domain(according to a cell ID). The PCFICH is transmitted at the first OFDMsymbol of a subframe all the time. Accordingly, when receiving asubframe, the receiver first confirms PCFICH information, and recognizesthe number of OFDM symbols needed for PDCCH transmission, such that itcan receive control information transmitted over a PDCCH.

Physical Hybrid-ARQ Indicator Channel (PHICH)

FIG. 10 shows the positions of PCFICH and PHICH generally applied to aspecific bandwidth. ACK/NACK information for uplink data transmission istransmitted over a PHICH. A plurality of PHICH groups is constructed ina single subframe, and a plurality of PHICHs may be present in a singlePHICH group. Therefore, PHICH channels for multiple UEs are contained ina single PHICH group.

Referring to FIG. 10, allocating a PHICH to each UE of a plurality ofPHICH groups is achieved not only using a lowest physical resource block(PRB) index of a PUSCH resource allocation but also a cyclic shift (CS)index for a demodulation RS (DMRS) transmitted on a UL grant PDCCH. DMRSis an uplink reference signal, and is provided along with ULtransmission so as to perform channel estimation for demodulating ULdata. In addition, a PHICH resource is signaled as an index pair such as(n_(PHICH) ^(group),n_(PHICH) ^(seq)). In the index pair (n_(PHICH)^(group), n_(PHICH) ^(seq)) n_(PHICH) ^(group) denotes a PHICH groupnumber and n_(PHICH) ^(seq) denotes an orthogonal sequence index in thecorresponding PHICH group. n_(PHICH) ^(group) and n_(PHICH) ^(seq) aredefined as shown in the following equation 1.n _(PHICH) ^(group)=(I _(PRB) _(_) _(RA) ^(lowest) ^(_) ^(index) +n_(DMRS))mod N _(PHICH) ^(group)n _(PHICH) ^(seq)(└I _(PRB) _(_) _(RA) ^(lowest) ^(_) ^(index) /N_(PHICH) ^(group) ┘+n _(DMRS))mod 2N _(SF) ^(PHICH)  [Equation 1]

In Equation 1, n_(DMRS) denotes a cyclic shift of a DMRS used for uplinktransmission related to a PHICH, N_(SF) ^(PHICH) denotes the size of aspreading factor sued for a PHICH, I_(PRB) _(_) _(RA) ^(lowest) ^(_)^(index) is the lowest PRB index of uplink resource allocation, andN_(PHICH) ^(group) denotes the number of PHICH groups. N_(PHICH)^(group) can be obtained using the following equation 2.

$\begin{matrix}{N_{PHICH}^{group} = \left\{ \begin{matrix}\left\lceil {N_{g}\left( {N_{RB}^{DL}/8} \right\rceil} \right. & {{for}\mspace{14mu}{normal}\mspace{14mu}{cyclic}\mspace{14mu}{prefix}} \\{2 \cdot \left\lceil {N_{g}\left( {N_{RB}^{DL}/8} \right\rceil} \right.} & {{for}\mspace{14mu}{extended}\mspace{14mu}{cyclic}\mspace{14mu}{prefix}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

In Equation 2, N_(g) denotes information regarding the amount of PHICHresources transmitted on a physical broadcast channel (PBCH), and N_(g)is 2 bits long and is denoted by N_(g) ∈{1/6, 1/2, 1, 2}.

In addition, examples of orthogonal sequences defined in the legacy 3GPPLTE Release 8/9 are shown in the following table 2.

TABLE 2 Orthogonal sequence Sequence index Normal cyclic prefix Extendedcyclic prefix n_(PHICH) ^(seq) N_(SF) ^(PHICH) = 4 N_(SF) ^(PHICH) = 2 0[+1 +1 +1 +1] [+1 +1] 1 [+1 −1 +1 −1] [+1 −1] 2 [+1 +1 −1 −1] [+j +j] 3[+1 −1 −1 +1] [+j −j] 4 [+j +j +j +j] — 5 [+j −j +j −j] — 6 [+j +j −j−j] — 7 [+j −j −j +j] —

FIG. 11 shows a downlink resource element position mapped to a PHICHgroup. A PHICH group may be constructed in different time domains (i.e.,different OFDM Symbols (OSs)) of a single subframe according to a PHICHduration.

Physical Downlink Control Channel (PDCCH)

Control information transmitted over a PDCCH may have different sizesand usages of control information according to a downlink controlinformation (DCI) format, and the PDCCH size may be changed according tocoding rate. For example, DCI formats for use in the legacy 3GPP LTERelease 9/9 can be defined as shown in the following table 3.

TABLE 3 DCI format Objectives 0 Scheduling of PUSCH 1 Scheduling of onePDSCH codeword 1A Compact scheduling of one PDSCH codeword 1BClosed-loop single-rank transmission 1C Paging, RACH response anddynamic BCCH 1D MU-MIMO 2 Scheduling of rank-adapted closed-loop spatialmultiplexing mode 2A Scheduling of rank-adapted open-loop spatialmultiplexing mode 3 TPC commands for PUCCH and PUSCH with 2 bit poweradjustments 3A TPC commands for PUCCH and PUSCH with single bit poweradjustments

The DCI format of Table 3 may be independently applied to each UE.PDCCHs of multiple UEs may be multiplexed in one subframe. PDCCH of eachUE may be independently channel-coded such that a CRC (Cyclic RedundancyCheck) may be added to the PDCCH. The CRC is masked as a unique ID foreach UE in such a manner that each UE can receive its own PDCCH.However, the UE does not know where its own PDCCH is transmitted, suchthat the UE performs blind detection (also called blind decoding) of allPDCCHs of the corresponding DCI format for each subframe until one PDCCHhaving a UE ID is received. A basic resource allocation unit of thePDCCH is a control channel element (CCE), and one CCE is composed of 9REGs. One PDCCH may be composed of 1, 2, 4, or 8 CCEs. The PDCCHconfigured according to each UE is interleaved and mapped to a controlchannel region of each subframe according to the CCE-to-RE mapping rule.The RE position mapped to a CCE may be changed according to the numberof OFDM symbols for a control channel of each subframe, the number ofPHICH groups, a Tx antenna, a frequency shift, and the like.

Uplink Retransmission

Uplink retransmission may be indicated through the above-mentioned PHICHand DCI format 0 (DCI format for scheduling PUSCH transmission). The UEreceives ACK/NACK information for previous uplink transmission through aPHICH, such that it can perform synchronous non-adaptive retransmission.Alternatively, the UE receives an uplink grant from a base station (BS)through DCI format 0 PDCCH, such that it can perform synchronousadaptive retransmission.

The term “synchronous retransmission” means that retransmission isperformed at a predetermined time (for example, the (n+k)^(th) subframe)after lapse of a transmission time (for example, the n^(th) subframe) ofone data packet (where k may be set to 4). In the case of retransmissioncaused by a PHICH and retransmission caused by a UL grant PDCCH,synchronous retransmission is performed.

In the case of non-adaptive retransmission in which retransmission isperformed through a PHICH, the same frequency resource (for example, aphysical resource block (PRB)) and retransmission method (for example, amodulation method or the like) as those of previous transmission areapplied to retransmission. On the other hand, in the case of adaptiveretransmission in which retransmission is performed through a UL grantPDCCH, the frequency resource and transmission method in whichretransmission is performed according to scheduling control informationindicated by a UL grant may be established in a different way from thoseof previous transmission.

If the UE simultaneously receives a PHICH and a UL grant PDCCH, thePHICH is disregarded and UL transmission can be performed according tocontrol information of a UL grant PDCCH. A new data indicator (NDI) iscontained in a UL grant PDCCH (for example, DCI format 0). If an NDI bitis toggled more than a previous NDI value, the UE decides that previoustransmission was successfully achieved such that it can transmit newdata. On the other hand, although the UE receives an ACK for previoustransmission through a PHICH, if an NDI value is not toggledsimultaneously with PHICH reception or if an NDI value is not toggled ata UL grant PDCCH to be received after PHICH reception, the UE isconfigured not to flush a buffer for previous transmission.

Uplink Transmission Structure

FIG. 12 is a block diagram illustrating a transmitter for use in aSingle Carrier Frequency-Division Multiple Access (SC-FDMA) system.

Referring to FIG. 12, a serial-to-parallel (SP) converter 1201 convertsone block composed of N symbols input to the transmitter into parallelsignals. An N-point DFT module 1202 spreads the parallel signals and asubcarrier mapping module 1203 maps the spread parallel signals to afrequency area. Each subcarrier signal is a linear combination of Nsymbols. An M-point Inverse Fast Fourier Transform (IFFT) module 1204converts signals mapped to a frequency domain into time-domain signals.A parallel-to-serial converter 1205 converts the time-domain signals toa serial signal and adds a CP to the serial signal. The DFT processingof the N-point DFT module 1202 compensates for the effects of the IFFTprocessing of the M-point IFFT module 1204 to a certain degree. TheSC-FDMA scheme may also be referred to as DFT-s-OFDMA(DFT-spread-OFDMA). The signals input to the DFT module 1202 have a lowPeak-to-Average Power Ratio (PAPR) or Cubic Metric (CM). However, thesignals have a high PAPR after the DFT processing. The IFFT signalsoutput from the IFFT module 1204 may have a low PAPR gain. That is, theSC-FDMA scheme can transmit signals through the remaining parts otherthan a non-linear distortion interval of the power amplifier (PA), suchthat implementation costs of transmission can be reduced.

FIG. 13 shows a signal mapping scheme in which a DFT processed signal ismapped to a frequency domain. One of the two schemes shown in FIG. 13 isperformed so that output signals of the SC-FDMA transmitter can satisfysingle carrier properties. FIG. 13(a) shows the localized mapping schemein which output signals from the DFT module 1202 are mapped only to aspecific part of the subcarrier region. FIG. 13(b) shows the distributedmapping scheme in which output signals from the DFT module 1202 aredistributed and mapped to the entire subcarrier region. The legacy 3GPPLTE Release 8/9 system is defined to use the localized mapping scheme.

FIG. 14 is a block diagram illustrating transmission processing of areference signal (RS) for demodulating a transmission signal based onthe SC-FDMA scheme. A data part for use in the legacy 3GPP LTE Release8/9 system is defined as follows. That is, after a signal generated in atime domain is DFT-processed and converted into a frequency-domainsignal, the signal is mapped to subcarriers and IFFT-processed (See FIG.12). A reference signal (RS) for use in the legacy 3GPP LTE Release 8/9system is defined as follows. That is, RS is directly generated in thefrequency domain without DFT processing, is mapped to subcarriers, andis IFFT-processed, such that a CP is attached to the IFFT result andthen transmitted.

FIG. 15 shows the position of a symbol mapped to a reference signal (RS)in a subframe structure based on the SC-FDMA scheme. FIG. 15(a) showsthat a reference signal (RS) is located at a fourth SC-FDMA symbol ofeach of two slots of a single subframe in case of a normal CP. FIG.15(b) shows that a reference signal (RS) is located at a third SC-FDMAsymbol of each of two slots of one subframe in case of an extended CP.

FIGS. 16 to 19 are conceptual views illustrating the clusteredDFT-s-OFDMA scheme. Referring to FIGS. 16 to 19, clustered DFT-s-OFDMAis a modification of the above-described SC-FDMA, in which a DFT signalis divided into a plurality of sub-blocks and mapped to positionsseparated from each other in the frequency domain.

FIG. 16 illustrates a clustered DFT-s-OFDMA scheme in a single carriersystem. For example, a DFT output may be divided into Nsb sub-blocks(sub-block #0 to sub-block #Nsb-1). The sub-blocks, sub-block #0 tosub-block #Nsb-1 are mapped to positions spaced from each other in thefrequency domain on a single carrier (e.g. a carrier having a bandwidthof 20 MHz). Each sub-block may be mapped to a frequency area in thelocalized mapping scheme.

FIGS. 17 and 18 illustrate clustered DFT-s-OFDMA schemes in amulti-carrier system.

FIG. 18 illustrates an example of generating a signal through one IFFTmodule, when multiple carriers are contiguously configured (i.e. therespective frequency bands of the multiple carriers are contiguous) anda specific subcarrier spacing is aligned between adjacent carriers. Forexample, a DFT output may be divided into Nsb sub-blocks (sub-block #0to sub-block #Nsb-1) and the sub-blocks, sub-block #0 to sub-block#Nsb-1 may be mapped, in one-to-one correspondence, to the ComponentCarriers (CCs), CC #0 to CC #Nsb-1 (each CC may have, for example, abandwidth of 20 MHz). Each sub-block may be mapped to a frequency areain the localized mapping scheme. The sub-blocks mapped to the respectiveCCs may be converted into a time signal through a single IFFT module.

FIG. 18 illustrates an example of generating signals through a pluralityof IFFT modules, when multiple carriers (or multiple cells) arenon-contiguously configured (i.e. the respective frequency bands of themultiple carriers are non-contiguous). For example, a DFT output may bedivided into Nsb sub-blocks, sub-block #0 to sub-block #Nsb-1 and thesub-blocks, sub-block #0 to sub-block #Nsb-1 may be mapped, in aone-to-one correspondence, to CCs, CC #0 to CC #Nsb-1 (each CC (or eachcell) may have, for example, a bandwidth of 20 MHz). Each sub-block maybe mapped to a frequency area in the localized mapping scheme. Thesub-blocks mapped to the respective CCs may be converted intotime-domain signals through respective IFFT modules.

If the clustered DFT-s-OFDMA scheme for a single carrier illustrated inFIG. 16 is intra-carrier (or intra-cell) DFT-s-OFDMA, it may be saidthat the clustered DFT-s-OFDMA schemes for multiple carriers (ormultiple cells) illustrated in FIGS. 17 and 18 are inter-carrier (orinter-cell) DFT-s-OFDMA. Intra-carrier DFT-s-OFDMA and inter-carrierDFT-s-OFDMA may be used in combination.

FIG. 12 illustrates a chunk-specific DFT-s-OFDMA scheme in which DFT,frequency-domain mapping, and IFFT processing are performed on a chunkbasis. Chunk-specific DFT-s-OFDMA may also be referred to as Nx SC-FDMA.A code block resulting from code block segmentation is divided intochunks and the chunks are channel-encoded and modulated individually.The modulated signals are subjected to DFT, frequency-domain mapping,and IFFT and the IFFT signals are summed and then a CP is added theretoin the same manner as described with reference to FIG. 12. The NxSC-FDMA scheme illustrated in FIG. 19 is applicable to both a case ofcontiguous multiple carriers (or contiguous multiple cells) and a caseof non-contiguous multiple carriers.

MIMO System

FIG. 20 is a block diagram illustrating a MIMO system including multipleTx antennas and multiple Rx antennas. Individual blocks of FIG. 20conceptually illustrate functions or operations of the transmitter andreceiver for MIMO transmission.

The channel encoder shown in FIG. 20 illustrates that a redundancy bitis attached to input data bits so that influence caused by noise from achannel can be greatly reduced. The mapper converts data bit informationinto data symbol information. The S/P converter converts serial datainto parallel data. The MIMO encoder converts a data symbol into atime-spatial signal. Multiple antennas of the transmitter are used totransmit time-spatial signals over a channel, and multiple antennas ofthe receiver are used to receive signals through a channel.

The MIMO decoder shown in FIG. 20 converts the received time-spatialsignal into respective data symbols. The P/S converter converts aparallel signal into a serial signal. The demapper converts a datasymbol into data bit information. The channel decoder illustrates thedecoding operation of a channel code, and estimates the decodedresultant data.

The above-mentioned MIMO Tx/Rx system may have one or more codewordsaccording to spatial multiplexing rate. One case in which only onecodeword spatially is used is referred as a single codeword (SCW)structure, and the other case in which multiple codewords (MCW) are usedis referred to as an MCW structure.

FIG. 21(a) is a block diagram illustrating a transmitter of a MIMOsystem including an SCW structure, and FIG. 21(b) is a block diagramillustrating a transmitter of a MIMO system including an MCW structure.

Codebook-Based Precoding Scheme

The precoding scheme for properly distributing transmission informationto respective antennas according to channel condition or the like so asto support MIMO transmission can be used. The codebook based precodingscheme allows each of a transmitter and a receiver to predetermine anaggregate or set of precoding matrices, the receiver measures channelinformation received from the transmitter, feeds back the mostappropriate precoding matrix (i.e., a precoding matrix index (PMI)) tothe transmitter, and the transmitter can apply the appropriate precodingto signal transmission on the basis of the PMI result. In this way, thecodebook based precoding scheme can select an appropriate precodingmatrix from among predetermined precoding matrix sets. As a result,although optimum precoding is not always applied, feedback overhead canbe more reduced than feedback overhead obtained when optimum precodinginformation is explicitly fed back to actual channel information.

FIG. 22 is a conceptual diagram illustrating codebook based precoding.

In accordance with the codebook based precoding scheme, a transceivermay share codebook information including a predetermined number ofprecoding matrices according to a transmission rank, the number ofantennas, etc. That is, if feedback information is infinite, theprecoding-based codebook scheme may be used. The receiver measures achannel state through a received signal, so that an infinite number ofpreferred precoding matrix information (i.e., an index of thecorresponding precoding matrix) may be fed back to the transmitter onthe basis of the above-mentioned codebook information. For example, thereceiver may select an optimum precoding matrix by measuring an ML(Maximum Likelihood) or MMSE (Minimum Mean Square Error) scheme.Although the receiver shown in FIG. 22 transmits precoding matrixinformation for each codeword to the transmitter, the scope or spirit ofthe present invention is not limited thereto.

Upon receiving feedback information from the receiver, the transmittermay select a specific precoding matrix from a codebook on the basis ofthe received information. The transmitter that has selected theprecoding matrix performs a precoding operation by multiplying theselected precoding matrix by as many layer signals as the number oftransmission ranks, and may transmit each precoded Tx signal over aplurality of antennas. In the precoding matrix, the number of rows isidentical to the number of antennas, and the number of columns isidentical to the rank value. Since the rank value is identical to thenumber of layers, the number of columns is identical to the number oflayers. For example, assuming that the number of Tx antennas is set to 4and the number of Tx layers is set to 2, the precoding matrix may beconfigured in the form of a (4×2) matrix. Information transmittedthrough individual layers in the precoding matrix can be mapped toindividual layers.

If the receiver receives the precoded signal from the transmitter as aninput, it performs inverse processing of the precoding having beenconducted in the transmitter so that it can recover the reception (Rx)signal. Generally, the precoding matrix satisfies a unitary matrix (U)such as (U*U^(H)=I), so that the inverse processing of theabove-mentioned precoding may be conducted by multiplying a Hermitianmatrix (P^(H)) of the precoding matrix H used in precoding of thetransmitter by the reception (Rx) signal.

For example, Table 4 shows a codebook for use in downlink transmissionin which 2Tx antennas are used in 3GPP LTE Release 8/9, and Table 5shows a codebook for use in downlink transmission in which 4Tx antennasare used in 3GPP LTE Release 8/9.

TABLE 4 Codebook Number of rank index 1 2 0$\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ 1 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}$ 3 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ —

TABLE 5 Codebook Number of layers υ index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1−1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{squareroot over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁^({12})/{square root over (2)} W₁ ^({123})/{square root over (3)} W₁^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over(2)} W₂ ^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1−j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{squareroot over (3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)}−j (1 − j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square rootover (2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1− j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

In Table 5, W_(n) ^({s}) is obtained from the set {s} composed of theequation denoted by W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n). Here, I isa (4×4) unitary matrix, and u_(n) is given by Table 5.

As can be seen from Table 4, the codebook for 2Tx antennas includes atotal of 7 precoding vectors/matrices. In this case, the unitary matrixis used for an open-loop system, and there are a total of 6 precodingvectors/matrices for precoding the closed-loop system. The codebook for4Tx antennas shown in Table 5 includes a total of 64 precodingvectors/matrices.

The above-mentioned codebook has common properties, for example,constant modulus (CM) property, nested property, and constrainedalphabet property. According to the CM property, individual elements ofall precoding matrices contained in the codebook do not include thevalue of 0, and are configured to have the same size. The nestedproperty means that a low-rank precoding matrix is composed of a subsetof a specific column of high-rank precoding matrices. The constrainedalphabet property means that alphabets of individual elements of all theprecoding matrices contained in the codebook are composed of

$\left\{ {{\pm 1},{\pm j},{\pm \frac{\left( {1 + j} \right)}{\sqrt{2}}},{\pm \frac{\left( {{- 1} + j} \right)}{\sqrt{2}}}} \right\}.$

Feedback Channel Structure

Basically, since a base station (BS) for use in an FDD system does notrecognize information of a downlink channel, channel information fedback from a user equipment (UE) is used for downlink transmission. Inthe case of the legacy 3GPP LTE Release 8/9 system, downlink channelinformation may be fed back through a PUCCH, or downlink channelinformation may be fed back through a PUSCH. In case of a PUCCH, channelinformation is periodically fed back. In case of a PUSCH, channelinformation is aperiodically fed back upon receiving a request from thebase station (BS). In case of feedback of channel information, channelinformation for the entirety of the allocated frequency bands (i.e.,wideband (WB)) may be fed back, and channel information for apredetermined number of RBs (i.e., subband (SB)) may be fed back.

Extended Antenna Configuration

FIG. 23 exemplarily shows 8Tx antennas. FIG. 23(a) shows an exemplarycase in which independent channels are constructed without grouping Nantennas. Generally, a Uniform Linear Array (ULA) is shown in FIG.23(a). Multiple antennas are spatially spaced apart from each other,such that the space of the transmitter and/or receiver needed forconstructing independent channels may be insufficient.

FIG. 23(b) shows a paired ULA in which one pair is composed of twoantennas. Related channels may be used between two antennas paired witheach other, and channels independent of other-paired antennas may alsobe used.

On the other hand, whereas the legacy 3GPP LTE Release 8/9 system uses 4Tx antennas on downlink, the 3GPP LTE Release 10 system can use 8 Txantennas on downlink. In order to apply the extended antennaconfiguration, multiple Tx antennas must be installed in an insufficientspace, and ULA antenna configurations shown in FIGS. 23(a) and 23(b) maybe considered inappropriate. Therefore, a method for applying dual-pole(or cross-pole) antenna configuration may be used as shown in FIG.23(c). In the case of constructing the above-mentioned Tx antennas,although a distance (d) between antennas is relatively short, antennacorrelation is reduced so that high-productivity data transmission maybe possible.

Codebook Structures

As described above, the transmitter shares the predefined codebook withthe receiver, and the amount of overhead needed when the receiver feedsback precoding information to be used for MIMO transmission from thetransmitter can be reduced, resulting in implementation of efficientprecoding.

As one example for constructing the pre-defined codebook, the precodermatrix can be constructed using a Discrete Fourier Transform (DFT)matrix or Walsh matrix. Alternatively, various types of precoders may becombined with the phase shift matrix or the phase shift diversitymatrix, etc.

When constructing the DFT-matrix based codebook, a (n×n) DFT matrix maybe defined as shown in Equation 3.

$\begin{matrix}{{{{DFTn}\text{:}\mspace{14mu}{D_{n}\left( {k,\ell} \right)}} = {\frac{1}{\sqrt{n}}{\exp\left( {{- j}\; 2\;\pi\; k\;{\ell/n}} \right)}}},\; k,\;{\ell - 0},1,\ldots\mspace{14mu},{n - 1}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

The DFT matrix of Equation 3 includes only one matrix for a specificsize (n). Therefore, in order to properly utilize a variety of precodingmatrices according to a situation, a rotated version of a DFTn matrixmay be additionally configured and used. The following equation 4represents the exemplary rotated DFTn matrix.

$\begin{matrix}{{{{rotated}\mspace{20mu}{DFTn}\text{:}\mspace{14mu}{D_{n}^{({G,g})}\left( {k,\ell} \right)}} = {\frac{1}{\sqrt{n}}{\exp\left( {{- j}\; 2\;\pi\;{{k\left( \;{\ell + {g/G}} \right)}/n}} \right)}}},\mspace{79mu} k,\;{\ell = 0},1,\ldots\mspace{14mu},{n - 1},\mspace{79mu}{g = 0},1,\ldots\mspace{14mu},{G.}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

When constructing the DFT matrix as shown in Equation 4, G rotated DFTnmatrices can be generated, and the generated matrices can satisfy DFTmatrix properties.

A Householder-based codebook structure will hereinafter be described indetail. The Householder-based codebook structure indicates a codebookcomposed of Householder matrices. The Householder matrix is used inHouseholder transformation. The Householder transformation may be a kindof linear transformation, and may be used for QR decomposition. The QRdecomposition means that a certain matrix is decomposed into anorthogonal matrix (QW) and an upper triangular matrix (R). The uppertriangular matrix (R) means a square in which all lower components ofthe main diagonal components are set to zero. An example of the (4×4)Householder matrix is shown in Equation 5.

$\begin{matrix}{{M_{1} = {{I_{4} - {2\; u_{0}u_{1}^{H}l{u_{0}}^{2}}} = {\frac{1}{\sqrt{4}}*\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}}}},\mspace{79mu}{u_{0}^{T} = \begin{bmatrix}1 & {- 1} & {- 1} & {- 1}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

The (4×4) unitary matrix having CM characteristics can be generated byHouseholder transformation. Referring to the codebook for 4Tx antennasshown in Table 5, the (n×n) precoding matrix is generated throughHouseholder transformation, and can be used as a precoding matrix fortransmitting a rank lower than ‘n’ using the column subset of thegenerated precoding matrix.

Codebook for 8Tx Antennas

A feedback scheme used in the legacy 3GPP LTE Release 8/9 system isextended and then applied to the 3GPP LTE Release-10 system havingextended antenna configuration (for example, 8 Tx antennas). Forexample, channel state information (CSI) (such as a rank indicator (RI),a precoding matrix index (PMI), channel quality information (CQI), etc.)can be fed back. A method for designing a dual-precoder based feedbackcodebook applicable to a system supporting the extended antennaconfiguration will hereinafter be described in detail. In thedual-precoder based feedback codebook, in order to indicate the precoderto be used for MIMO transmission of the transmitter, the receiver cantransmit a PMI to the transmitter, and the precoding matrix can beindicated by a combination of two different PMIs. That is, the receiverfeeds back two different PMIs (i.e., a first PMI and a second PMI) tothe transmitter, and the transmitter decides a precoding matrixindicated by a combination of a first PMI and a second PMI and appliesthe decided precoding matrix to MIMO transmission.

In a dual-precoder based feedback design, 8Tx antenna MIMO transmission,SU-MIMO (Single User-MIMO) and MU-MIMO (Multiple User-MIMO) supportingadaptability of various antenna configurations, a codebook designreference, a codebook size, etc. can be considered.

As a codebook applied to 8Tx antenna MIMO transmission, it may bepossible to design a feedback codebook that supports only SU-MIMO incase of Rank 2 or more, is optimized for SU-MIMO and MU-MIMO in case ofa Rank of less than Rank 2, and is suitable for various antennaconfigurations.

In MU-MIMO, UEs participating in MU-MIMO can be separated from eachother in a correlation domain. Therefore, there is a need for thecodebook for MU-MIMO to be correctly operated at a high-correlationchannel. DFT vectors provide superior performance over ahigh-correlation channel, such that a DFT vector may be contained in thecodebook set extending to Rank-2. In addition, in a high scatteringpropagation environment (e.g., an indoor environment having numerousreflected waves) capable of generating numerous spatial channels, theSU-MIMO operation may be more appropriately used as the MIMOtransmission scheme. Therefore, the codebook for a rank higher thanRank-2 can be designed to obtain superior performance for discriminatingbetween multiple layers.

In the precoder for MIMO transmission, it is preferable that oneprecoder has superior performance in various antenna configurations(low-correlation antenna configuration, high-correlation antennaconfiguration, cross-pole antenna configuration, etc.). In thedeployment of 8 Tx antennas, a cross-pole array having an antennainterval of 4λ may be configured as the low-correlation antennaconfiguration, a ULA having an antenna interval of 0.5λ may beconfigured as the high-correlation antenna configuration, and across-pole array having an antenna interval of 0.5λ may be configured asthe cross-pole antenna configuration. The DFT-based codebook structurecan provide superior performance to the high-correlation antennaconfiguration. Meanwhile, block diagonal matrices may be moreappropriately used for cross-pole antenna configuration as necessary.Therefore, assuming that a diagonal matrix is applied to the codebookfor 8Tx antennas, it may be possible to construct the codebook capableof providing superior performance to all antenna configurations.

The codebook can be designed to satisfy a unitary codebook, CM property,finite alphabets, an appropriate codebook size, nested property, etc.The above-mentioned codebook design can be applied to the 3GPP LTERelease 8/9 codebook, and can also be applied to the 3GPP LTE Release-10codebook supporting an extended antenna configuration.

In association with the codebook size, it is necessary to increase thecodebook size so as to sufficiently support advantages obtained by 8 Txantennas. In order to obtain a sufficient precoding gain from 8 Txantennas under a low-correlation environment, a large-sized codebook(for example, a codebook composed of at least 4 bits for Rank-1 andRank-2) may be needed. In order to obtain precoding gain under ahigh-correlation environment, the above 4-bit sized codebook may beconsidered sufficient. However, in order to implement MU-MIMOmultiplexing gain, the codebook size for Rank-1 or Rank-2 may beincreased.

Based on the above-mentioned description, the codebook structure for 8Tx antennas can be defined as follows.

In order to support multi-granular feedback, the 8Tx-antenna codebookstructure can be defined by a Kroneker product

of two base matrices. The Kroneker product

is an operation of two matrices each having a predetermined size, suchthat a block matrix can be obtained as the operation result of theKroneker product

. For example, the Kroneker product (A

B) of the (m×n) matrix A and the (p×q) matrix B can be denoted by thefollowing equation 6. In Equation 6, a_(mn) is an element of the matrixA, and b_(pq) is an element of the matrix B.

$\begin{matrix}{{A \otimes B} = \left\lbrack \begin{matrix}{a_{11}b_{11}} & {a_{11}b_{12}} & \ldots & {a_{11}b_{1q}} & \ldots & \ldots & {a_{1n}b_{11}} & {a_{1n}b_{12}} & \ldots & {a_{1n}b_{1q}} \\{a_{11}b_{21}} & {a_{11}b_{22}} & \ldots & {a_{11}b_{2q}} & \ldots & \ldots & {a_{1n}b_{21}} & {a_{1n}b_{22}} & \ldots & {a_{1n}b_{2q}} \\\vdots & \vdots & \ddots & \vdots & \mspace{11mu} & \; & \vdots & \vdots & \ddots & \vdots \\{a_{11}b_{p\; 1}} & {a_{11}b_{p\; 2}} & \ldots & {a_{11}b_{pq}} & \ldots & \ldots & {a_{1n}b_{p\; 1}} & {a_{1n}b_{p\; 2}} & \ldots & {a_{1n}b_{pq}} \\\vdots & \vdots & \; & \vdots & {\ddots\;} & \; & \vdots & \vdots & \; & \vdots \\\vdots & \vdots & \; & \vdots & \; & {\;\ddots} & \vdots & \vdots & \; & \vdots \\{a_{m\; 1}b_{11}} & {a_{m\; 1}b_{12}} & \ldots & {a_{m\; 1}b_{1q}} & \ldots & \ldots & {a_{mn}b_{11}} & {a_{mn}b_{12}} & \ldots & {a_{mn}b_{1q}} \\{a_{m\; 1}b_{21}} & {a_{m\; 1}b_{22}} & \ldots & {a_{m\; 1}b_{2q}} & \ldots & \ldots & {a_{mn}b_{21}} & {a_{mn}b_{22}} & \ldots & {a_{mn}b_{2q}} \\\vdots & \vdots & \ddots & \vdots & \; & \; & \vdots & \vdots & \ddots & \vdots \\{a_{m\; 1}b_{p\; 1}} & {a_{m\; 1}b_{p\; 2}} & \ldots & {a_{m\; 1}b_{pq}} & \ldots & \ldots & {a_{m\; n}b_{p\; 1}} & {a_{m\; n}b_{p\; 2}} & \ldots & {a_{m\; n}b_{p\; q}}\end{matrix} \right\rbrack} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

The following equation 7 shows that the codebook structure is configuredas the Kroneker product of two base matrices (W₁ ^((m)) and W₂.W=W ₂

W ₁ ^((m))  [Equation 7]

In Equation 7, a first base matrix W₁ ^((m)) (where m is a transmissionrank) may be used for beamforming of contiguous co-polarized antennas.For the first base matrix, a few types of codebook may be used. Forexample, the codebook (i.e., a codebook of Table 5) for performingdownlink MIMO transmission through 4Tx antennas defined in 3GPP LTERelease 8/9 may be used as a first base matrix. Alternatively, a DFTmatrix may be used as the first base matrix.

The second base matrix W₂ of Equation 7 may be used to adjust a relativephase between orthogonal polarizations. The matrix shown in Equation 8may be used as the second base matrix. For example, the Rank-2 precodingmatrix of a codebook (i.e., a codebook of Table 4) for performingdownlink MIMO transmission through 2Tx antennas defined in 3GPP LTERelease 8/9 may be used as a second base matrix.

$\begin{matrix}{W_{2} = \begin{bmatrix}1 & 1 \\e^{j\frac{\pi\; n}{N}} & {- e^{j\frac{\pi\; n}{N}}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

A feedback codebook for 8 Tx antennas according to transmission rank canbe defined as shown in Table 6.

TABLE 6 Rank-1 W¹ = W² (:, 1), W¹ = W² (:, 2) Rank-2 W² = W₂ 

 W₁ ¹ Rank-3 W³ = W⁴ (:, 1:3) Rank-4 W⁴ = W₂  

 W₁ ² Rank-5 W⁵ = W⁶ (:, 1:5) Rank-6 W⁶ = W₂  

 W₁ ³ Rank-7 W⁷ = W⁸ (:, 1:7) Rank-8 W⁸ = W₂ 

 W₁ ⁴

In Table 6, W²(;,x) is an X^(th) column of a matrix W². That is, W¹ maybe composed of a first column of the matrix W² or may be composed of asecond column of the matrix W². Similarly, W^(n)(;,x:y) denotes columnsfrom an x^(th) column to y^(th) column. For example, W³ may be composedof columns from a first column to a third column.

As shown in Table 6, a feedback codebook for an even rank (Rank 2, Rank4, Rank 6, or Rank 8) may be generated by a Kroneker product of two basematrices. For example, a Rank-2 codebook W² (8×2 matrix) for 8Txantennas is denoted by W²=W₂

W₁ ¹. Here, W₂ denotes a (2×2) matrix of a Rank-2 codebook (See Table 4)for 2 Tx antennas shown in Equation 8, and denotes a (4×1) matrix of aRank-1 codebook (See Table 5) for 4 Tx antennas. In addition, a Rank-4codebook W⁴ (i.e., a (8×4) matrix) for 8 Tx antennas is denoted by W⁴=W₂

W₁ ². Here, W₂ denotes a (2×2) matrix of a Rank-2 codebook (See Table 4)for 2 Tx antennas shown in Equation 8, and W₁ ² denotes a (4×2) matrixof a Rank-2 codebook (See Table 5) for 4 Tx antennas.

As shown in Table 6, a feedback codebook for an odd rank (Rank 1, Rank3, Rank 5, or Rank 7) may be composed of a subset of upper rankcodebooks. For example, the Rank-1 codebook for 8 Tx antennas may becomposed of a subset selected from the Rank-2 codebook for 8 Txantennas. The Rank-3 codebook for 8 Tx antennas may be composed of asubset selected from the Rank-4 codebook for 8 Tx antennas.Alternatively, the Rank-5 codebook for 8 Tx antennas may be composed ofa subset selected from the Rank-6 codebook for 8 Tx antennas. The Rank-7codebook for 8 Tx antennas may be composed of a subset selected from theRank-8 codebook for 8 Tx antennas. The above-mentioned codebookconfiguration shown in Table 6 is disclosed for illustrative purposesonly, and a method for generating a codebook for each rank shown inTable 6 may be independently applied to respective ranks, or may also besimultaneously applied to respective ranks. In addition, therelationship between codebooks of respective ranks shown in Table 6 (forexample, the relationship between a low-rank codebook composed of ahigh-rank codebook subset and a high-rank codebook) may be independentlyapplied to respective ranks, or may also be simultaneously applied torespective ranks.

In association with multi-granular feedback application, a method forapplying the Kroneker product to a method for constructing the codebookfor 8 Tx antennas using a combination of two base matrices has alreadybeen disclosed as described above. Hereinafter, a method forconstructing a combination of two base matrices using an inner productwill be described in detail. A specific format using an inner product oftwo base matrices is represented by Equation 9.W={tilde over (W)} ₁ {tilde over (W)} ₂  [Equation 9]

If a codebook for 8 Tx antennas is represented as an inner product, afirst base matrix can be represented by a diagonal matrix shown in Table10 for a co-polarized antenna group.

$\begin{matrix}{{\overset{\sim}{W}}_{1} = {\begin{bmatrix}W_{1} & 0 \\0 & W_{1}\end{bmatrix}\left( {W_{1}\text{:}4 \times N} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

In addition, if a second base matrix is used to adjust a relative phasebetween polarities, the second base matrix can be denoted by an identitymatrix. In association with a higher rank for the codebook for 8 Txantennas, the second base matrix can be denoted by the followingequation 11. As can be seen from Equation 11, the relationship between acoefficient (1) of a first row of the second base matrix and acoefficient (a or −a) of a second row of the second base matrix is usedto reflect adjustment of the aforementioned relative phase.

$\begin{matrix}{{\overset{\sim}{W}}_{2} = {\begin{bmatrix}I & I \\{aI} & {- {aI}}\end{bmatrix}\left( {I\text{:}N \times N} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

Therefore, the codebook for 8 Tx antennas can be denoted by Equation 12using an inner product of the first base matrix and the second basematrix.

$\begin{matrix}{W = {{\begin{bmatrix}W_{1} & 0 \\0 & W_{1}\end{bmatrix}\begin{bmatrix}I & I \\{aI} & {- {aI}}\end{bmatrix}} = \begin{bmatrix}W_{1} & W_{1} \\{aW}_{1} & {- {aW}_{1}}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

The codebook based on the inner product of Equation 12 can be simplyrepresented using the Kroneker product shown in the following equation13.W=W ₂

W ₁(W ₁:4×N,W ₂:2×M)  [Equation 13]

In Equation 13, the precoding matrix contained in a codebook W includes(4×2) rows and (N×M) columns. Accordingly, the precoding matrix may beused as a codebook for 8Tx-antenna (N×M) Rank transmission. For example,assuming that the precoding codebook for 8Tx-antenna Rank-R transmissionis configured and W₂ is composed of a (2×M) matrix, an N value of thematrix W₁ is denoted by R/M. For example, when constructing theprecoding codebook for 8Tx-antenna Rank-4 transmission, if W₂ iscomposed of a (2×2) matrix (i.e., M=2) (for example, a matrix ofEquation 8), W₁ may be denoted by a (4×2) matrix (i.e., N=R/M=4/2=2)(e.g., a DFT matrix).

Generation of Multiple-Codebook Based Precoder

The precoding operation for use in MIMO transmission may be consideredto be the operation for mapping Tx signals to antenna(s) throughlayer(s). That is, Y Tx layers (or Y Tx streams) may be mapped to X Txantennas through an (X×Y) precoding matrix.

In order to construct the (N_(t)×R) precoding matrix when R streams(i.e., a Rank R) are transmitted through N_(t) Tx antennas, at least oneprecoding matrix index (PMI) is fed back from the receiver so that thetransmitter can construct the precoder matrix. The following equation 14shows an exemplary codebook composed of n_(c) matrices.P _(N) _(t) _(×R)(k)∈{P ₁ ^(N) ^(t) ^(×R) ,P ₂ ^(N) ^(t) ^(×R) ,P ₃ ^(N)^(t) ^(×R) , . . . ,P _(n) _(c) ^(N) ^(t) ^(×R)}  [Equation 14]

In Equation 14, k is a specific resource index (subcarrier index,virtual resource index, or subband index). Equation 14 may be configuredas shown in the following equation 15.

$\begin{matrix}{{{P_{N_{t} \times R}(k)} = \begin{bmatrix}P_{{M_{t} \times R},1} \\P_{{M_{t} \times R},2}\end{bmatrix}},{N_{t} = {2 \cdot M_{t}}}} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

In Equation 15, P_(M) _(t) _(×R,2) may be implemented by shifting P_(M)_(t) _(×R,1) by a specific complex weight w₂. Therefore, when adifference between P_(M) _(t) _(×R,1) and P_(M) _(t) _(×R,2) is denotedby a specific complex weight, the following equation 16 can be obtained.

$\begin{matrix}{{P_{N_{t} \times R}(k)} = \begin{bmatrix}{w_{1} \cdot P_{{M_{t} \times R},1}} \\{w_{2} \cdot P_{{M_{t} \times R},1}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack\end{matrix}$

In addition, Equation 16 can be denoted by the following equation 17using the Kroneker product.

$\begin{matrix}{{P_{{N_{t} \times R},n,m}(k)} = {{\begin{bmatrix}w_{1} \\w_{2}\end{bmatrix}P_{{M_{t} \times R},1}} = {W_{n}P_{m}}}} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack\end{matrix}$

In Equation 17, the partial precoding matrix

$\left\lbrack \left. \quad\begin{matrix}w_{1} \\w_{2}\end{matrix} \right\rbrack \right.$or P_(M) _(t) _(×R,1) may be independently fed back from the receiver.The transmitter may be implemented by configuring the precoder ofEquation 16 or 17 using each feedback information. When using the formatof Equation 16 or 17, W is always configured in the form of a (2×1)vector, and may be configured as a codebook of Equation 18.

$\begin{matrix}{{W\; \in \begin{bmatrix}1 \\e^{j\frac{2\;\pi}{N}i}\end{bmatrix}},{i = 0},\ldots\mspace{14mu},{N - 1}} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack\end{matrix}$

In Equation 18, N is a total number of precoding vectors, and i may beused as a vector index. In order to minimize feedback overhead as wellas to obtain proper performance, i may be set to any one of 2, 4, or 8.In addition, P_(M) _(t) _(×R,1) may be composed of either a codebook for4 Tx antennas or a codebook for 2 Tx antennas. In association with theabove-mentioned description, the codebook of Table 4 or 5 (i.e., thecodebook for 2 or 4 Tx antennas defined in 3GPP LTE Release 8/9) may beused, and the codebook may also be configured in a rotated DFT format.

In addition, the matrix W may be configured as a (2×2) matrix. Anexample of the 2×2 W matrix is shown in the following equation 19.

$\begin{matrix}{{{P_{{N_{t} \times R},n,m}(k)} = {{\begin{bmatrix}w_{1} & w_{3} \\w_{2} & w_{4}\end{bmatrix}P_{{M_{t} \times R},1}} = {W_{n}P_{m}}}},{N_{t} = {2 \cdot M_{t}}}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack\end{matrix}$

In Equation 19, if a maximum rank of the codebook P_(M) _(t) _(×R,1) isset to R, the range of the codebook design may be extended up to a Rankof 2R. For example, if the codebook of Table 4 is used as P_(M) _(t)_(×R,1) a maximum rank may be extended up to 4 (R=4) according toEquation 17. On the other hand, a maximum rank may be extended up to 8(2R=8) as can be seen from equation 18. Therefore, it may be possible toconstruct a precoder that is capable of performing 8×8 transmission in asystem including 8 Tx antennas. In this case, W may be configured as acodebook of Equation 20.

$\begin{matrix}{{W\; \in \begin{bmatrix}1 & 1 \\e^{j\frac{2\;\pi}{N}i} & {- e^{j\frac{2\;\pi}{N}i}}\end{bmatrix}},{i = 0},\ldots\mspace{14mu},{N - 1}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack\end{matrix}$

The precoder configuration methods shown in Equations 17 and 18 may bedifferently applied according to individual ranks. For example, thescheme of Equation 17 is applied to Rank 4 or less (R≤4), and the schemeof Equation 18 is applied to Rank 5 or higher (R≥5). Alternatively, thescheme of Equation 17 may be applied only to Rank 1 (R=1), and thescheme of Equation 18 may be applied to the remaining ranks (Rank 2 ormore (R≥2)). In association with Equation 17 and Equation 18, W and Pmay be fed back to have properties shown in the following table 7.

TABLE 7 Case W/P Frequency granularity 1 One of two matrices is fed backto a subband, and the remaining one matrix may be fed back to awideband. Frequency granularity 2 One of two matrices is fed back to abest-M band, and the remaining one matrix may be fed back to a wideband.Time granularity One of two matrices is fed back at intervals of N, andthe remaining one matrix is fed back at intervals of M. Feedback channel1 One of two matrices is fed back to PUSCH, and the remaining one matrixis fed back to PUCCH. Feedback channel 2 If a feedback to PUSCH isperformed, one (e.g., W) of two matrices is fed back to a subband, andthe remaining one matrix (e.g., P) is fed back to a wideband. If afeedback to PUCCH is performed, both W and P can be fed back to awideband. Unequal protection One (e.g., P) of two matrices can beencoded with a higher reliability coding rate, and the remaining onematrix (e.g., W) can be encoded with a lower reliability coding rate.Alphabet restriction 1 Alphabets of the matrix W may be limited to BPSK,and alphabets of the matrix P may be limited to QPSK or 8PSK. Alphabetrestriction 2 Alphabets of the matrix W may be limited to QPSK, andalphabets of the matrix P may be limited to QPSK or 8PSK.

It may be possible to construct the codebook using Equation 17 andEquation 18. However, it may be impossible to construct the precoder onthe condition that two kinds of combinations are not used according tosituation. In order to solve the above-mentioned problem, the precodercan be constructed as shown in the following equation 21.

$\begin{matrix}{{P_{{N_{t} \times N_{t}},n,m} = {{\begin{bmatrix}w_{1} & w_{3} \\w_{2} & w_{4}\end{bmatrix}P_{M_{t} \times M_{t}}} = {W_{n}P_{m}}}},{N_{t} = {2 \cdot M_{t}}}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack\end{matrix}$

A precoder for an exemplary case (R=N_(t)) is configured using P_(N)_(t) _(×N) _(t) obtained from Equation 21. Here, the case (R=N_(t))indicates that a rank value is identical to the number of Tx antennas,and the column subset of the configured precoder may be used for a lowerrank. When constructing the precoder as described above, nestedproperties are satisfied so that CQI calculation can be simplified. InEquation 21, P_(N) _(t) _(×N) _(t) _(,n,m) is a precoder in case ofR=N_(t). For example, a subset composed of the 0^(th) and 2^(nd) columnsof the precoder P_(N) _(t) _(×N) _(t) _(,n,m) may be used as theprecoder of R=2, and may be denoted by P_(N) _(t) _(×N) _(t) _(,n,m)(0,2). Here, P_(M) _(t) _(×M) _(t) may be composed of a rotated DFTmatrix or other types of codebook.

On the other hand, in order to increase a diversity gain under anopen-loop environment, beam diversity gain can be maximized by replacinga precoder with another precoder according to a specific resource on thebasis of the above-mentioned precoder. For example, if the precoder ofEquation 17 is used, the scheme for applying the precoder according to aspecific resource can be denoted by the following equation 22.P _(N) _(t) _(×R,n,m)(k)=W _(k mod n) _(c)

P _(k mod m) _(c)   [Equation 22]

In Equation 22, k is a specific resource region. The precoding matrixfor the specific resource region k is determined by the modulo operationshown in Equation 22. In Equation 22, n_(c) is the size of a codebookfor the matrix W, and m_(c) is the size of a codebook for the matrix P.Each of n_(c) and m_(c) may correspond to each subset.

When applying cycling of both matrices as shown in Equation 22,diversity gain can be maximized and complexity can be increased.Therefore, long-term cycling may be applied to a specific matrix, andshort-term cycling may be applied to the remaining matrices.

For example, the modulo operation may be applied to the matrix Waccording to a PRB index, and the modulo operation may be applied to thematrix P according to a subframe index. Alternatively, the modulooperation may be applied to the matrix W according to a subframe index,and the modulo operation may be applied to the matrix P according to aPRB index.

In another example, the modulo operation may be applied to the matrix Waccording to a PRB index, and the modulo operation may be applied to thematrix P according to a subband index. Alternatively, the modulooperation may be applied to the matrix W according to a subframe index,and the modulo operation may be applied to the matrix P according to aPRB index.

In addition, precoder cycling based on the modulo operation is appliedto only one of two matrices, and the other matrix may be fixed.

When constructing the precoder using two matrices, the codebookstructure may be denoted by an inner product as shown in Equations 9 to12, or the codebook structure may also be denoted by a Kroneker productshown in Equation 13.

Detailed Information of Codebook Structure for 8 Tx Antennas

Based on the precoder structure applicable to the system including amaximum of 8 Tx antennas, the embodiments of the present invention fordetailed information (precoder size, factor component, etc.) throughwhich precoding can be applied to a MIMO system will hereinafter bedescribed. In addition, the exemplary precoding structures capable ofsupporting various antenna configurations will hereinafter be described.

Codebook Structure

The codebook for 8 Tx antennas may be configured by a combination of twobase matrices. In association with the aforementioned description, twocombination methods can be used. One of the two combination methods isimplemented by the inner product, and the other combination method isimplemented by the Kroneker product.

First, the codebook denoted by an inner product of two base matrices isshown in the following equation 23.W={tilde over (W)} ₁ {tilde over (W)} ₂  [Equation 23]

If the codebook for 8 Tx antennas is represented in the form of an innerproduct, a first base matrix for the co-polarized antenna group can berepresented by a diagonal matrix shown in Equation 24.

$\begin{matrix}{{\overset{\sim}{W}}_{1} = {\begin{bmatrix}W_{1} & 0 \\0 & W_{1}\end{bmatrix}\left( {W_{1}\text{:}4 \times N} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack\end{matrix}$

In addition, if a second base matrix is used to adjust a relative phasebetween polarities, the second base matrix can be denoted by an identitymatrix. In addition, for a high rank of a codebook for 8 Tx antennas,the second base matrix can be denoted as shown in Equation 25. InEquation 25, the relationship between a coefficient ‘1’ of a first rowof the second base matrix and a coefficient (a) of a second row of thesecond base matrix is used to adjust the aforementioned relative phase.

$\begin{matrix}{{\overset{\sim}{W}}_{2} = {\begin{bmatrix}I \\{a\; I}\end{bmatrix}\left( {I\text{:}N \times N} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 25} \right\rbrack\end{matrix}$

Therefore, the codebook for 8 Tx antennas can be represented by thefollowing equation 26 using inner products of the first base matrix andthe second base matrix.

$\begin{matrix}{{W = {{\begin{bmatrix}W_{1} & 0 \\0 & W_{1}\end{bmatrix}\begin{bmatrix}I \\{a\; I}\end{bmatrix}} = \begin{bmatrix}W_{1} \\{aW}_{1}\end{bmatrix}}}\;} & \left\lbrack {{Equation}\mspace{14mu} 26} \right\rbrack\end{matrix}$

The codebook denoted by the inner product as shown in Equation 26 can berepresented using the Kroneker product shown in the following equation27.W=W ₂

W ₁(W ₁:4×N,W ₂:2×M)  [Equation 27]

DFT Based Codebook

A (n×n) DFT matrix can be defined as shown in the following equation 28.

$\begin{matrix}{{{{DFT\_ N}\text{:}\mspace{20mu}{D_{N}\left( {k,n} \right)}} = {\frac{1}{\sqrt{N}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/N}} \right)}}},k,{n = 0},1,\ldots\mspace{14mu},{N - 1}} & \left\lbrack {{Equation}\mspace{14mu} 28} \right\rbrack\end{matrix}$

For example, when generating the codebook for 8Tx-antenna MIMOtransmission, the simplest codebook can be denoted by the followingequation 29.

$\begin{matrix}{{{{DFT\_}8\text{:}\mspace{20mu}{D_{8}\left( {k,n} \right)}} = {\frac{1}{\sqrt{8}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}},k,{n = 0},1,\ldots\mspace{14mu},7} & \left\lbrack {{Equation}\mspace{14mu} 29} \right\rbrack\end{matrix}$

In the DFT_8 codebook shown in Equation 29, 8 columns can be defined asthe precoding weights having different responses.

When constructing the spatial channel, a response of a Tx antenna underULA environment can be denoted by the following equation 30.

$\begin{matrix}{{a_{t}(\theta)} = {\frac{1}{\sqrt{8}}\left\lbrack {1\; e^{{{- j}\; 2\pi\frac{d}{\lambda}s\; i\;{n{(\theta)}}}\mspace{11mu}}e^{{{- j}\; 2\pi\frac{2d}{\lambda}s\; i\;{n{(\theta)}}}\mspace{11mu}}e^{{{- j}\; 2\pi\frac{3d}{\lambda}s\; i\;{n{(\theta)}}}\mspace{11mu}}e^{{{- j}\; 2\pi\frac{4d}{\lambda}s\; i\;{n{(\theta)}}}\mspace{11mu}}e^{{{- j}\; 2\pi\frac{5d}{\lambda}s\; i\;{n{(\theta)}}}\mspace{11mu}}e^{{{- j}\; 2\pi\frac{6d}{\lambda}s\; i\;{n{(\theta)}}}\mspace{11mu}}e^{{{- j}\; 2\pi\frac{7d}{\lambda}s\; i\;{n{(\theta)}}}\mspace{11mu}}} \right\rbrack}} & \left\lbrack {{Equation}\mspace{14mu} 30} \right\rbrack\end{matrix}$

In Equation 30, d is a spacing or distance between antennas, and λ is awavelength of an intermediate frequency. A phase θ is an angle between aplane wave and an antenna array, and may be denoted by DoA (Direction OfArrival) or AoA (Angle Of Arrival). In a high-correlation (or highlycorrelated) channel, a Tx antenna response based on the codebookobtained by Equation 29 may be obtained by an inner product related toEquation 30. For the aforementioned reasons, the vector of Equation 30may also be referred to as the steering vector for either a transmission(Tx) direction or a reception (Rx) direction according to an antennaarray.

FIG. 24 shows an antenna response of the DFT_8 codebook shown inEquation 29. In FIG. 24, a vertical axis represents the amplitude of anantenna frequency response, and a horizontal axis represents the valueof θ denoted by a radian value. 8 parabolic parts each having a maximumfrequency response are shown in FIG. 24. Each parabolic part mayindicate an antenna response constructed by a column vector of the DFT_8codebook. A first column vector of the DFT_8 codebook has a maximumantenna response at θ=0° (0 rad), a second column vector has a maximumantenna response at θ=14° (about 0.24 rad), a third column vector has amaximum antenna response at θ=30° (about 0.52 rad), a fourth columnvector has a maximum antenna response at θ=49° (about 0.85 rad), a fifthcolumn vector has a maximum antenna response at θ=90° (about 1.57 rad),a sixth column vector has a maximum antenna response at θ=−49° (about−0.85 rad), a seventh column vector has a maximum antenna response atθ=−30° (about −0.52 rad), and an eighth column vector has a maximumantenna response at θ=−14° (about 0.24 rad). In accordance with thepresent invention, the antenna response may be referred to as a beam forconvenience of description and better understanding of the presentinvention. That is, DFT_8 may generate beams of 0°, 14°, 30°, 49°, 90°,−49°, −30°, or −14°.

In order to form more dense beams, the DFT matrix may be configured tohave a small reference phase. For example, an oversampled DFT matrixshown in Equation 31 may be used as necessary.

$\begin{matrix}{{{{{DFT\_ N}^{*}a\text{:}\mspace{20mu}{D_{N^{*}a}\left( {k,n} \right)}} = {\frac{1}{\sqrt{N}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/\left( {N^{*}a} \right)}} \right)}}},\;{k = 0},1,\ldots\mspace{14mu},{N - 1}}{{n = 0},1,\ldots\mspace{14mu},{\left( {N^{*}a} \right) - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 31} \right\rbrack\end{matrix}$

In Equation 31, N is the number of Tx antennas, a is an oversamplingcoefficient, k is an antenna index, and n is a codebook index. Thecodebook based on Equation 31 may form (N×a) beams having differentphases using N Tx antennas. For example, assuming that oversampling isapplied two times when constructing the DFT codebook for 8 Tx antennas,the following equation 32 may be used.

$\begin{matrix}{{{{{DFT\_}16\text{:}\mspace{20mu}{D_{16}\left( {k,n} \right)}} = {\frac{1}{\sqrt{8}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/\left( {8^{*}2} \right)}} \right)}}},\;{k = 0},1,\ldots\mspace{14mu},8}{{n = 0},1,\ldots\mspace{14mu},15}} & \left\lbrack {{Equation}\mspace{14mu} 32} \right\rbrack\end{matrix}$

16 vectors for 8 Tx antennas can be constructed using the aforementionedEquation 32, and associated antenna responses can be represented asshown in FIG. 25.

The codebooks shown in Equations 31 and 32 are appropriate for ULAantenna configuration.

On the other hand, as a codebook structure for effectively supportingthe dual-polarization antenna configuration, block-diagonal-shapedcodebook structures shown in Equations 22, 23 to 27 may be preferablyused as necessary. In case of using the block-diagonal-shaped matrix,the elements arranged at diagonal positions may be composed of acodebook supporting 4 Tx antennas. In addition, a codebook supporting 2Tx antennas may be used to combine two co-polarization antennas. In thiscase, as a codebook for 4 Tx antennas and a codebook for 2 Tx antennas,a DFT-shaped codebook may be used. Alternatively, a codebook defined in3GPP LTE Release 8/9 may be used as shown in Tables 4 and 5.Specifically, when using the DFT-shaped codebook, the codebook shown inthe following equation 33 can be used.

$\begin{matrix}{{{{{DFT\_}2\text{:}\mspace{20mu}{D_{2}\left( {k,n} \right)}} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/2}} \right)}}},\;{k = 0},1,{n = 0},1}{{{{DFT\_}4\text{:}\mspace{20mu}{D_{4}\left( {k,n} \right)}} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/4}} \right)}}},\;{k = 0},1,2,3}{{n = 0},1,2,3}} & \left\lbrack {{Equation}\mspace{14mu} 33} \right\rbrack\end{matrix}$

In Equation 33, DFT_2 may generate a (2×2) matrix, and DFT_4 maygenerate a (4×4) matrix, as shown in the following equation 34.

$\begin{matrix}{{{{DFT\_}2\text{:}\mspace{14mu} W_{2}} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}{{{DFT\_}4\text{:}\mspace{20mu} W_{1}} = \;\begin{bmatrix}1 & 1 & 1 & 1 \\1 & {- j} & {- 1} & j \\1 & {- 1} & 1 & {- 1} \\1 & j & {- 1} & {- j}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 34} \right\rbrack\end{matrix}$

In Equation 34, W₂ may be composed of a matrix having two vectors, andW₁ may be composed of a matrix having four vectors. When constructingthe 8Tx antenna codebook shown in Equation 17 using W₁ and W₂ shown inEquation 34 as base codebooks, the following equation 35 can beobtained.

$\begin{matrix}{W = {{W_{2} \otimes W_{1}} = \left\lbrack \begin{matrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\1 & {- j} & {- 1} & j & 1 & {- j} & {- 1} & j \\1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\1 & j & {- 1} & {- j} & 1 & j & {- 1} & {- j} \\1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\1 & {- j} & {- 1} & j & {- 1} & j & 1 & {- j} \\1 & {- 1} & 1 & {- 1} & {- 1} & 1 & {- 1} & 1 \\1 & j & {- 1} & {- j} & {- 1} & {- j} & 1 & j\end{matrix} \right\rbrack}} & \left\lbrack {{Equation}\mspace{14mu} 35} \right\rbrack\end{matrix}$

The codebook shown in Equation 35 is used as the codebook for 8 Txantennas, and may be composed of a matrix including 8 vectors. Theantenna response for the ULA antenna configuration composed of 8 Txantennas of the above-mentioned codebook can be represented as shown inFIG. 26.

Referring to FIG. 26, the codebook obtained by a combination of DFT 4and DFT_2 has only four antenna responses whereas it has 8 elements,because the codebook elements composed of two codebooks are 90 degreesout of phase with each other. A minimum phase value capable of beingrepresented by any one matrix element of two base matrices may bedetermined to be a minimum interval of an antenna response capable ofbeing represented by a codebook. DFT_4 may represent a phase of 90°, andDFT_2 may be extended to a phase of 180°. Therefore, provided that DFT_8having more dense spacing for the 4Tx antenna codebook is used, thespacing of a frequency response capable of being represented isincreased. The 4Tx antenna codebook having been oversampled two timesaccording to Equation 31 can be generated as shown in the followingequation 36.

$\begin{matrix}{{{{{DFT\_}8\text{:}\mspace{14mu}{D_{8}\left( {k,n} \right)}} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}},{k = 0},1,2,3}{{n = 0},1,\ldots\mspace{14mu},7}} & \left\lbrack {{Equation}\mspace{14mu} 36} \right\rbrack\end{matrix}$

In Equation 36, DFT_8 can generate a (4×8) matrix, as shown in thefollowing equation 37.

                                     [Equation  37] $\begin{matrix}{W_{1} = {{\quad\quad}{\frac{1}{\sqrt{4}}\left\lbrack \begin{matrix}e^{j\;{0 \cdot {0/8}}} & e^{j\;{0 \cdot {1/8}}} & e^{j\;{0 \cdot {2/8}}} & e^{j\;{0 \cdot {3/8}}} & e^{j\;{0 \cdot {4/8}}} & e^{j\;{0 \cdot {5/8}}} & e^{j\;{0 \cdot {6/8}}} & e^{j\;{0 \cdot {7/8}}} \\e^{j\;{1 \cdot {0/8}}} & e^{j\;{1 \cdot {1/8}}} & e^{j\;{1 \cdot {2/8}}} & e^{j\;{1 \cdot {3/8}}} & e^{j\;{1 \cdot {4/8}}} & e^{j\;{1 \cdot {5/8}}} & e^{j\;{1 \cdot {6/8}}} & e^{j\;{1 \cdot {7/8}}} \\e^{j\;{2 \cdot {0/8}}} & e^{j\;{2 \cdot {1/8}}} & e^{j\;{2 \cdot {2/8}}} & e^{j\;{2 \cdot {3/8}}} & e^{j\;{2 \cdot {4/8}}} & e^{j\;{2 \cdot {5/8}}} & e^{j\;{2 \cdot {6/8}}} & e^{j\;{2 \cdot {7/8}}} \\e^{j\;{3 \cdot {0/8}}} & e^{j\;{3 \cdot {1/8}}} & e^{j\;{3 \cdot {2/8}}} & e^{j\;{3 \cdot {3/8}}} & e^{j\;{3 \cdot {4/8}}} & e^{j\;{3 \cdot {5/8}}} & e^{j\;{3 \cdot {6/8}}} & e^{j\;{3 \cdot {7/8}}}\end{matrix} \right\rbrack}}} & \;\end{matrix}$

8 vectors, each of which is composed of 4 elements, are represented byEquation 37. The matrix shown in Equation 37 may also be combined with adiagonal matrix having a phase shift as shown in the following equation38.

$\begin{matrix}{W_{1} = {{\frac{1}{\sqrt{4}}\left\lbrack \begin{matrix}e^{j\;{0 \cdot 4 \cdot {m/8}}} & 0 & 0 & 0 \\0 & e^{j\;{1 \cdot 4 \cdot {m/8}}} & 0 & 0 \\0 & 0 & e^{j\;{2 \cdot 4 \cdot {m/8}}} & 0 \\0 & 0 & 0 & e^{j\;{3 \cdot 4 \cdot {m/8}}}\end{matrix} \right\rbrack}{\quad{\left\lbrack \begin{matrix}e^{j\;{0 \cdot {0/8}}} & e^{j\;{0 \cdot {1/8}}} & e^{j\;{0 \cdot {2/8}}} & e^{j\;{0 \cdot {3/8}}} \\e^{j\;{1 \cdot {0/8}}} & e^{j\;{1 \cdot {1/8}}} & e^{j\;{1 \cdot {2/8}}} & e^{j\;{1 \cdot {3/8}}} \\e^{j\;{2 \cdot {0/8}}} & e^{j\;{2 \cdot {1/8}}} & e^{j\;{2 \cdot {2/8}}} & e^{j\;{2 \cdot {3/8}}} \\e^{j\;{3 \cdot {0/8}}} & e^{j\;{3 \cdot {1/8}}} & e^{j\;{3 \cdot {2/8}}} & e^{j\;{3 \cdot {3/8}}}\end{matrix} \right\rbrack,\mspace{79mu}{m = 0},1}}}} & \left\lbrack {{Equation}\mspace{14mu} 38} \right\rbrack\end{matrix}$

The 4Tx-antenna codebook (i.e., DFT_8 of Equation 36) having beenoversampled two times is used as a single base matrix (W₁), and the2Tx-antenna codebook (i.e., DFT_2 of Equation 33) configured to useDFT_2 is used as the other base matrix (W₂). The 8Tx-antenna codebookgenerated using Equation 17 can be represented by the following equation39.

$\begin{matrix}{{{DFT\_}2\text{:}}{{W_{2} = {{D_{2}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/2}} \right)}}}},\begin{matrix}{{k = 0},1} & {{n = 0},1}\end{matrix}}{{DFT\_}8\text{:}}{{W_{1} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}},{k = 0},1,2,{{3\mspace{14mu} n} = 0},1,\ldots\mspace{14mu},{{7W} = {W_{2} \otimes W_{1}}}}} & \left\lbrack {{Equation}\mspace{14mu} 39} \right\rbrack\end{matrix}$

The antenna response for the 8Tx-antenna codebook obtained by Equation39 can be represented as shown in FIG. 27.

The antenna response shown in FIG. 27 is identical to an antennaresponse shown in FIG. 24 (showing an antenna response of the8Tx-antenna codebook of Equation 29). The 8Tx-antenna codebook obtainedthrough Equation 39 is composed of 16 vectors, and the other 8Tx-antennacodebook obtained through Equation 29 is composed of 8 vectors. 8vectors from among the codebook of Equation 39 may be completelyidentical to 8 vectors from among the codebook of Equation 29, or signsof all the elements (i.e., 8 vectors) of the codebook of Equation 39 areinverted (that is, ‘+’ is inverted to ‘−’, and ‘−’ is inverted to ‘+’)so that the inverted result of the codebook of Equation 39 correspondsto the codebook of Equation 29. Therefore, the antenna response of thecodebook of Equation 39 may be identical to that of the codebook ofEquation 29 as necessary. In addition, 8 additional vectors are shown inEquation 39, and a beam formed by the 8 additional vectors has twosmall-sized antenna responses.

The base codebook shown in the following equations 40 to 53 can bedefined according to the oversampling factor.

$\begin{matrix}{{{{{DFT\_}2\text{:}\mspace{14mu} W_{2}} = {{D_{2}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/2}} \right)}}}},{k = 0},{{1\mspace{14mu} n} = 0},1}{{DFT\_}12\text{:}}\mspace{11mu}{W_{1} = {{D_{12}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/12}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},11} & \left\lbrack {{Equation}\mspace{14mu} 40} \right\rbrack \\{{{{{DFT\_}2\text{:}\mspace{14mu} W_{2}} = {{D_{2}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/2}} \right)}}}},\begin{matrix}{{k = 0},1} & {{n = 0},1}\end{matrix}}{{{DFT\_}16\text{:}\mspace{14mu} W_{1}} = {{D_{16}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/16}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},15} & \left\lbrack {{Equation}\mspace{14mu} 41} \right\rbrack \\{{{{{DFT\_}4\text{:}\mspace{14mu} W_{2}} = {{D_{4}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/4}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}2},3}{{{{DFT\_}4\text{:}\mspace{14mu}{D_{4}\left( {k,n} \right)}} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/4}} \right)}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}2},3}} & \left\lbrack {{Equation}\mspace{14mu} 42} \right\rbrack \\{{{{{DFT\_}4\text{:}\mspace{14mu} W_{2}} = {{D_{4}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/4}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}2},3}{{{{DFT\_}8\text{:}\mspace{14mu} W_{1}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},7}} & \left\lbrack {{Equation}\mspace{14mu} 43} \right\rbrack \\{{{{{DFT\_}4\text{:}\mspace{14mu} W_{2}} = {{D_{4}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/4}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}2},3}{{DFT\_}12\text{:}}\mspace{11mu}{{W_{1} = {{D_{12}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/12}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},11}} & \left\lbrack {{Equation}\mspace{14mu} 44} \right\rbrack \\{{{{{DFT\_}4\text{:}\mspace{14mu} W_{2}} = {{D_{4}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/4}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}2},3}{{DFT\_}16\text{:}}\;{{W_{1} = {{D_{16}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/16}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},15}} & \left\lbrack {{Equation}\mspace{14mu} 45} \right\rbrack \\{{{{{DFT\_}8\text{:}\mspace{14mu} W_{2}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},7}{{{{DFT\_}4\text{:}\mspace{14mu}{D_{4}\left( {k,n} \right)}} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/4}} \right)}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}2},3}} & \left\lbrack {{Equation}\mspace{14mu} 46} \right\rbrack \\{{{{{DFT\_}8\text{:}\mspace{14mu} W_{2}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},7}{{{{DFT\_}8\text{:}\mspace{14mu} W_{1}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},7}} & \left\lbrack {{Equation}\mspace{14mu} 47} \right\rbrack \\{{{{{DFT\_}8\text{:}\mspace{14mu} W_{2}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},7}{{DFT\_}12\text{:}}\;{{W_{1} = {{D_{12}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/12}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},11}} & \left\lbrack {{Equation}\mspace{14mu} 48} \right\rbrack \\{{{{{DFT\_}8\text{:}\mspace{14mu} W_{2}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},7}{{DFT\_}16\text{:}}\mspace{11mu}{{W_{1} = {{D_{16}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/16}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},}\end{matrix}1},\ldots\mspace{14mu},15}} & \left\lbrack {{Equation}\mspace{14mu} 49} \right\rbrack \\{{{{{DFT\_}16\text{:}\mspace{14mu} W_{2}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/16}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},15}{{{{DFT\_}4\text{:}\mspace{14mu}{D_{4}\left( {k,n} \right)}} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/4}} \right)}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}2},3}} & \left\lbrack {{Equation}\mspace{14mu} 50} \right\rbrack \\{{{{{DFT\_}16\text{:}\mspace{14mu} W_{2}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/16}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},15}{{{{DFT\_}8\text{:}\mspace{14mu} W_{1}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/8}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},7}} & \left\lbrack {{Equation}\mspace{14mu} 51} \right\rbrack \\{{{{{DFT\_}16\text{:}\mspace{14mu} W_{2}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/16}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},15}{{DFT\_}12\text{:}}\mspace{11mu}{{W_{1} = {{D_{12}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/12}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},11}} & \left\lbrack {{Equation}\mspace{14mu} 52} \right\rbrack \\{{{{{DFT\_}16\text{:}\mspace{14mu} W_{2}} = {{D_{8}\left( {k,n} \right)} = {\frac{1}{\sqrt{2}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/16}} \right)}}}},{\begin{matrix}{{k = 0},1} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},15}{{DFT\_}16\text{:}}\;{{W_{1} = {{D_{16}\left( {k,n} \right)} = {\frac{1}{\sqrt{4}}{\exp\left( {{- j}\; 2\;\pi\;{{kn}/16}} \right)}}}},{\begin{matrix}{{k = 0},1,2,3} & {{n = 0},1,}\end{matrix}\ldots}\mspace{14mu},15}} & \left\lbrack {{Equation}\mspace{14mu} 53} \right\rbrack\end{matrix}$

Equations 40 to 53 show the codebook formats generated when oversamplingis applied to the base codebook. Equations 40 to 53 can be representedin a matrix format. In addition, Equations 40 to 53 may also be combinedwith a phase diagonal matrix as necessary.

The codebook generated by a combination of the oversampled base matricesmay be composed of a high-resolution codebook. The above-mentionedcodebook may be composed of a codebook in which more dense beams areformed. In association with the above description, although feedbackoverhead is reduced, beam resolution may not be greatly deteriorated.Some indices are excluded from either the base matrix or the codebookformed by a combination of two base matrices (i.e., subsampling for thebase matrices or the codebook index is applied), such that feedback tothe remaining indices other than the some indices is performed and theprecoder can be determined according to the feedback result.

Assuming that the precoder is selected from among a certain matrix fromamong two base matrices, selecting the precoder from among other basematrices may be dependent upon the previously selected precoder.

FIGS. 28 to 43 illustrate antenna responses changing with anoversampling factor for each of two base matrices. Provided that theoversampling factor for the first base matrix is denoted by OS1 (OS1=1,2, 3 or 4) and the oversampling factor of the second base matrix isdenoted by OS2 (OS2=1, 2, 3 or 4), antenna responses (shown in FIGS. 28to 43) of respective combinations can be represented by the followingtable 8. For example, assuming that the oversampling factor for thefirst base matrix is denoted by OS1=3 and the oversampling factor forthe second base matrix is denoted by OS2=2, antenna responses shown inFIG. 37 can be obtained.

TABLE 8 OS1 OS2 1 2 3 4 1 FIG. 28 FIG. 32 FIG. 36 FIG. 40 2 FIG. 29 FIG.33 FIG. 37 FIG. 41 3 FIG. 30 FIG. 34 FIG. 38 FIG. 42 4 FIG. 31 FIG. 35FIG. 39 FIG. 43

In accordance with the above-mentioned embodiments of the presentinvention, when constructing the precoder codebook applied to a maximumof 8 Tx antenna transmission using two base matrices, feedback overheadcan be reduced and a high-performance codebook can be obtained. Inaddition, it may be possible to provide a codebook capable ofguaranteeing superior performance in various antenna configurations.

FIG. 44 is a flowchart illustrating a MIMO transmission and receptionmethod according to embodiments of the present invention. UL MIMOtransmission and reception methods according to the embodiments of thepresent invention will hereinafter be described with reference to FIG.44.

Referring to FIG. 44, a user equipment (UE) can transmit a first PMI anda second PMI to a base station (BS) and the BS can receive the first andsecond PMIs in step S4410. Prior to step S4410, the UE can generatechannel state information (CSI) (for example, RI/PMI/CQI) by measuring aDL channel from the BS. The UE can transmit a PMI to the BS as a CSIfeedback in step S4410. In order to prevent overhead of feedbackinformation caused by the increased Tx antenna (a maximum of 8 Txantennas) from being increased, DL MIMO transmission from the BS canindicate a precoding matrix to be used for DL transmission using acombination of two different PMIs (first and second PMIs).

The BS can determine the precoding matrix indicated by a combination ofthe first PMI and the second PMI using the codebook in step S4420. Sucha codebook may be constructed according to various examples of thepresent invention. The BS can map DL signals to R layers (where 1≤R≤8)in step S4430. The number R of layers is a rank value. The BS canperform precoding in step S4440. The precoding may correspond to theoperation for mapping Tx layers to antennas. The BS can map DL signalstransmitted through R layers to Tx antennas using the decided precodingmatrix in step S4420.

The BS can transmit a precoded DL signal (i.e., a signal mapped to theTx antenna) to the UE, and the UE can receive the precoded DL signalfrom the BS in step S4450. After performing step S4460, the UE performsprocessing of the received DL signal using the same precoding matrix asa precoding matrix applied to the BS, such that it can recover adownlink signal. For example, the UE performs inverse precoding thatmultiplies the Hermitian matrix of the precoding matrix by the receivedDL signal, such that it can recover a downlink signal.

An example of the codebook used by (or prestored in) the BS will bedescribed with reference to step S4420. For example, it is assumed thatthe BS includes 2·N transmit (Tx) antennas (where N is a naturalnumber). For example, the BS may include 8 Tx antennas.

In this case, the codebook for MIMO transmission through 2·N transmit(Tx) antennas may include matrices shown in Equation 54 for an evennumber R.

$\begin{matrix}\begin{bmatrix}W_{1} & W_{1} \\{a\; W_{1}} & {{- a}\; W_{1}}\end{bmatrix} & \left\lbrack {{Equation}\mspace{14mu} 54} \right\rbrack\end{matrix}$

The matrices of Equation 54 have characteristics related to Equation 12.For example, a is a specific value for adjusting a relative phase. Inaddition, since W₂ has the size of 2×2 as shown in Equation 12, W₁ maybe composed of N rows corresponding to half the number of Tx antennas,or may be composed of R/2 columns corresponding to half the number(rank) of Tx layers. In other words, W₁ may be composed of theN×(R/2)-sized matrix. In addition, W₁ may be composed of a DFT matrix.For example, W₁ may be composed of a matrix of the codebook for 4 Txantennas shown in Table 4.

If R is an even number, W₁ may be composed of a matrix [v1 . . .v(R/2)]. That is, W₁ may be composed of R/2 column vectors. For example,W₁ may be composed of two column vectors [v1 v2]. In this case, W₁ is anN×(R/2) matrix, and each of v1 . . . v(R/2) may be composed of an (N×1)matrix. In addition, each of v1 . . . v(R/2) may be composed of a DFTmatrix.

Therefore, assuming that the number of Tx layers is 4 (i.e., R=4), W₁may be represented by the following equation 55. W₁ may have the sameformat as the codebook of Rank 4 shown in Table 6.

$\begin{matrix}{\begin{bmatrix}{v\; 1} & {v\; 2} & {v\; 1} & {v\; 2} \\{{a \cdot v}\; 1} & {{a \cdot v}\; 2} & {{{- a} \cdot v}\; 1} & {{{- a} \cdot v}\; 2}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 55} \right\rbrack\end{matrix}$

In addition, the codebook according to the examples of the presentinvention may have nested properties. For example, assuming that thenumber of Tx layers is denoted by 3≤R≤7, the precoding matrix for Rlayers may be composed of a column subset of the precoding matrix of(R+1) layers. For example, as shown in Table 6, the codebook of Rank 7may be configured to exclude one column from the codebook of Rank 8, andthe codebook of Rank 5 may be configured to exclude one column from thecodebook of Rank 6. Alternatively, the codebook of Rank 3 may beconfigured to exclude one column from the codebook of Rank 4.

In association with a method for transmitting/receiving a codebook basedsignal as shown in FIG. 44, the contents described in theabove-mentioned embodiments may be used independently of each other ortwo or more embodiments may be simultaneously applied, and the sameparts may be omitted herein for convenience and clarity of description.

In addition, the principles of the present invention may also be appliedto UL MIMO transmission and reception according to the present inventionin association with not only MIMO transmission between a base station(BS) and a relay node (RN) (for use in a backhaul uplink and a backhauldownlink) but also MIMO transmission between an RN and a UE (for use inan access uplink and an access downlink).

FIG. 45 is a block diagram of a BS apparatus and a UE apparatusaccording to an embodiment of the present invention.

Referring to FIG. 11, a BS (or eNB) apparatus 4510 may include areception (Rx) module 4511, a transmission (Tx) module 4512, a processor4513, a memory 4514, and a plurality of antennas 4515. The plurality ofantennas 4515 may be contained in the BS apparatus supporting MIMOtransmission and reception. The reception (Rx) module 1111 may receive avariety of signals, data and information on uplink starting from the UE.The transmission (Tx) module 4512 may transmit a variety of signals,data and information on downlink for the UE. The processor 4513 mayprovide overall control to the BS apparatus 1110.

The BS apparatus 4510 according to one embodiment of the presentinvention may be constructed to transmit downlink signals through 2·N (Nbeing a natural number) Tx antennas. The memory 4514 of the BS apparatusmay store the codebook including the precoding matrix. The processor4513 of the BS apparatus may be configured to receive the first andsecond PMIs from the UE through the Rx module 4511. The processor 4513may be configured to decide the precoding matrix indicated by acombination of the first and second PMIs from the codebook stored in thememory 4514. The processor 4513 may be configured to map DL signals to Rlayers (where 1≤R≤8). The processor 4513 may be configured to precode DLsignals mapped to R layers using the precoding matrix. Through the Txmodule 4512, the processor 4513 may be configured to transmit theprecoded signals to the UE over 2·N Tx antennas. In this case, theprestored codebook may include the precoding matrices of Equation 54when R is an even number. As shown in Equation 54, W₁ is an N×(R/2)matrix, and a is a coefficient regarding the phase.

The processor 4513 of the BS apparatus 4510 processes informationreceived at the BS apparatus 4510 and transmission information. Thememory 4514 may store the processed information for a predeterminedtime. The memory 4514 may be replaced with a component such as a buffer(not shown).

Referring to FIG. 45, a UE apparatus 4520 may include a reception (Rx)module 4521, a transmission (Tx) module 4522, a processor 4523, a memory4524, and a plurality of antennas 4525. The plurality of antennas 4525may be contained in the UE apparatus supporting MIMO transmission andreception. The reception (Rx) module 4521 may receive a variety ofsignals, data and information on downlink starting from the eNB. Thetransmission (Tx) module 4522 may transmit a variety of signals, dataand information on uplink for the eNB. The processor 4523 may provideoverall control to the UE apparatus 4520.

The UE apparatus 4520 according to one embodiment of the presentinvention may be constructed to process downlink signals transmittedfrom the BS apparatus 4510 including 2·N (N is a natural number) Txantennas. The memory 4524 of the UE apparatus may store the codebookincluding the precoding matrix. The processor 4523 of the UE apparatusmay be configured to transmit the first and second PMIs indicating theprecoding matrix selected from the codebook stored in the memory 4524 tothe BS apparatus 4510 through the Rx module 4511. The processor 4523 maybe configured to receive a DL signal transmitted over 2·N Tx antennasthrough the Rx module 4521. In more detail, the DL signal is mapped to Rlayers (where 1≤R≤8) by the BS apparatus 4510, and is then precoded bythe precoding matrix indicated by a combination of the first PMI and thesecond PMI. The processor 4523 may be configured to process a DL signalusing the precoding matrix. In this case, the prestored codebook mayinclude precoding matrices of Equation 54 when R is an even number. Asshown in Equation 54, W₁ is an N×(R/2) matrix, and a is a coefficientregarding the phase.

The processor 4523 of the UE apparatus 4520 processes informationreceived at the UE apparatus 4520 and transmission information. Thememory 4524 may store the processed information for a predeterminedtime. The memory 4524 may be replaced with a component such as a buffer(not shown).

The specific configurations of the above eNB and UE apparatuses may beimplemented such that the various embodiments of the present inventionare performed independently or two or more embodiments of the presentinvention are performed simultaneously. Redundant matters will not bedescribed herein for clarity.

The BS apparatus 4510 shown in FIG. 45 may also be applied to a relaynode (RN) acting as a DL transmission entity or UL reception entity, andthe UE apparatus 4520 shown in FIG. 45 may also be applied to a relaynode (RN) acting as a DL reception entity or UL transmission entity.

The above-described embodiments of the present invention can beimplemented by a variety of means, for example, hardware, firmware,software, or a combination of them.

In the case of implementing the present invention by hardware, thepresent invention can be implemented with application specificintegrated circuits (ASICs), Digital signal processors (DSPs), digitalsignal processing devices (DSPDs), programmable logic devices (PLDs),field programmable gate arrays (FPGAs), a processor, a controller, amicrocontroller, a microprocessor, etc.

If operations or functions of the present invention are implemented byfirmware or software, the present invention can be implemented in theform of a variety of formats, for example, modules, procedures,functions, etc. The software codes may be stored in a memory unit sothat it can be driven by a processor. The memory unit is located insideor outside of the processor, so that it can communicate with theaforementioned processor via a variety of well-known parts.

The detailed description of the exemplary embodiments of the presentinvention has been given to enable those skilled in the art to implementand practice the invention. Although the invention has been describedwith reference to the exemplary embodiments, those skilled in the artwill appreciate that various modifications and variations can be made inthe present invention without departing from the spirit or scope of theinvention described in the appended claims. For example, those skilledin the art may use each construction described in the above embodimentsin combination with each other. Accordingly, the invention should not belimited to the specific embodiments described herein, but should beaccorded the broadest scope consistent with the principles and novelfeatures disclosed herein.

Those skilled in the art will appreciate that the present invention maybe carried out in other specific ways than those set forth hereinwithout departing from the spirit and essential characteristics of thepresent invention. The above exemplary embodiments are therefore to beconstrued in all aspects as illustrative and not restrictive. The scopeof the invention should be determined by the appended claims and theirlegal equivalents, not by the above description, and all changes comingwithin the meaning and equivalency range of the appended claims areintended to be embraced therein. Also, it will be obvious to thoseskilled in the art that claims that are not explicitly cited in theappended claims may be presented in combination as an exemplaryembodiment of the present invention or included as a new claim bysubsequent amendment after the application is filed.

INDUSTRIAL APPLICABILITY

The embodiments of the present invention are applicable to a variety ofmobile communication systems.

The invention claimed is:
 1. A method for transmitting a precodingmatrix indicator (PMI) by a user equipment (UE) in a Multiple-InputMultiple-Output (MIMO) system, the method comprising: configuring, bythe UE, a codebook including a plurality of precoding matricescorresponding to a number of layers, and transmitting, by the UE to abase station (BS), at least one PMI corresponding to at least oneprecoding matrix among the plurality of precoding matrices, wherein theplurality of precoding matrices are configured in the form of$\begin{bmatrix}W_{1} & W_{1} \\{a\; W_{1}} & {{- a}\; W_{1}}\end{bmatrix},$ and wherein W1 is configured as a matrix of [v1 v2], v1and v2 are an 4×1 matrix, and a is a coefficient of a phase.
 2. Themethod according to claim 1, wherein W₁ is a Discrete Fourier Transform(DFT) matrix.
 3. The method according to claim 1, wherein the pluralityof precoding matrices are configured in the form of$\left\lbrack \begin{matrix}{v\; 1} & {v\; 2} & {v\; 1} & {v\; 2} \\{{a \cdot v}\; 1} & {{a \cdot v}\; 2} & {{{- a} \cdot v}\; 1} & {{{- a} \cdot v}\; 2}\end{matrix} \right\rbrack.$
 4. A method for configuring a codebook by abase station (BS) in a Multiple-Input Multiple-Output (MIMO) system, themethod comprising: configuring, by the BS, the codebook, and thecodebook includes a plurality of precoding matrices corresponding to anumber of layers, and transmitting, by the BS to a user equipment (UE),a downlink signal applied to at least one precoding matrix among theplurality of precoding matrices, wherein the plurality of precodingmatrices are configured in the form of $\begin{bmatrix}W_{1} & W_{1} \\{a\; W_{1}} & {{- a}\; W_{1}}\end{bmatrix},$ and wherein W1 is configured as a matrix of [v1 v2], v1and v2 are an 4×1 matrix, and a is a coefficient of a phase.
 5. Themethod according to claim 4, wherein W₁ is a Discrete Fourier Transform(DFT) matrix.
 6. The method according to claim 4, wherein the pluralityof precoding matrices are configured in the form of$\left\lbrack \begin{matrix}{v\; 1} & {v\; 2} & {v\; 1} & {v\; 2} \\{{a \cdot v}\; 1} & {{a \cdot v}\; 2} & {{{- a} \cdot v}\; 1} & {{{- a} \cdot v}\; 2}\end{matrix} \right\rbrack.$
 7. A user equipment (UE) for transmitting aprecoding matrix indicator (PMI) in a Multiple-Input Multiple-Output(MIMO) system, the UE comprising: a radio frequency (RF) unit configuredto transmit and receive a radio signal with a base station (BS); aprocessor configured to: configure a codebook including a plurality ofprecoding matrices corresponding to a number of layers, and control theRF unit to transmit to the BS at least one PMI corresponding to at leastone precoding matrix among the plurality of precoding matrices, whereinthe plurality of precoding matrices are configured in the form of$\begin{bmatrix}W_{1} & W_{1} \\{a\; W_{1}} & {{- a}\; W_{1}}\end{bmatrix},$ and wherein W1 is configured as a matrix of [v1 v2],wherein v1 and v2 are an 4×1 matrix, and a is a coefficient of a phase.8. A base station (BS) for configuring codebook in a Multiple-InputMultiple-Output (MIMO) system, the BS comprising: a radio frequency (RF)unit configured to transmit and receive a radio signal with a userequipment (UE); a processor configured to: configure the codebook, andthe codebook includes a plurality of precoding matrices corresponding toa number of layers, and control to the RF unit to transmit a downlinksignal applied to at least one precoding matrix among the plurality ofprecoding matrices to the UE, wherein at plurality of precoding matricesare configured in the form of $\begin{bmatrix}W_{1} & W_{1} \\{a\; W_{1}} & {{- a}\; W_{1}}\end{bmatrix},$ and wherein W1 is configured as a matrix of [v1 v2], v1and v2 are an 4×1 matrix, and a is a coefficient of a phase.